Four factors have contributed to the consensus opinion that early sources dated John’s apocalyptic vision late in Domitian’s reign:
i. the lack of engagement with contrary evidence (Irenaeus, Tertullian, Acts of John).
ii. the claiming of ambiguous evidence for the late date (Clement Alex., Origen, Irenaeus).
iii. the lack of any differentiation concerning the chronological placement of John’s apocalyptic vision by the two earliest extant, non ambiguous sources of the Domitianic tradition (i.e. Eusebius and Victorinus).
iv. the citing of later writers who were dependent on Eusebius as though they were independent witnesses to the late date (Jerome).
Thus, the evidence is brought over to the Domitianic side:
i. Lack of Engagement with Contrary Data
Irenaeus placed the writing of John’s Gospel at the end of the first century (at the time that the heretic Cerinthus was spreading his teachings in the province of Asia). He noted that the sect of the Nicolaitans had spread the same doctrines in Asia “a long time previously” to this (Haer. 3.11.1).
Elsewhere he placed the Nicolaitans at the time when Revelation was written (Haer. 1.26.3). Revelation therefore also seems to have been placed by Irenaeus “a long time previously” to the writing of the Gospel at the end of the first century.
This argument from Irenaeus for the early date, first noted by J. O. F. Murray in 1914, has been discussed in two recent monographs  but has not yet to received a response from proponents of the late date.
It can be noted too that Hippolytus seems to have assumed the same chronology, for he claimed that Hymenaeus and Philetus, who were active in Asia late in Nero’s reign (2 Tim 2:17–18), were following the teachings of Nicolas, the founder of the sect.
According to Tertullian, John was immersed into a vat of boiling oil but emerged unhurt, before being sent into exile. He thus speaks of Rome as the place
where Peter attains to the suffering of the Lord, where Paul is crowned with the departure of John [i.e. is beheaded], where the apostle John, after he was plunged into boiling oil, having suffered nothing, is exiled to an island.Tertullian, Praescr. 36.
Some scholars think that Tertullian implies that all three apostles suffered at the same time. Perhaps, though late-daters point out that this cannot be proven with certainty.
However, the discussion does not end there; Jerome quoted Tertullian (presumably from a lost work) to the effect that John was placed in boiling oil in Nero’s reign:
moreover, Tertullian relates that, having been thrown into a terracotta jar of burning oil by Nero (a Nerone), he came out cleaner and more vigorous than when he entered.Jerome, Jov. 1.26.
By comparing Jerome’s quotation and Tertullian himself, we can conclude that John was placed (according to Tertullian) in the boiling oil by Nero, and that upon emerging from it he was sent into exile.
Tertullian’s Text Amended
The evidence that Tertullian placed John’s exile in Nero’s reign is often overlooked, no doubt largely on account of the decision by Vittori, the sixteenth-century editor, to replace “by Nero,” the reading found in all the manuscripts, with “at Rome” in Jerome’s quotation.
This change leaves Jerome’s statement with no chronological implications for Tertullian’s story of the boiling oil.
Vittori explains that he made this amendment because Tertullian associated the boiling oil with the exile, and “this happened in Domitian’s reign.”
The Acts of John
The second- or third-century Acts of John depicts John as travelling throughout the province of Asia (four years in Smyrna alone), visiting the churches and appointing bishops (as in Clement below); it culminates in an account of John’s burial, without any mention of the exile. If the exile was related at all, it would have been mentioned in the lost beginning, as Lalleman noted.
Two pieces of evidence suggest that it had been so related:
i. the extant text begins with John sailing to Miletus, which would have been the natural stopping point from Patmos en route to Ephesus.
ii. the surviving evidence seems to indicate that in the original narrative of the Acts of John (much of which has not survived), John visited all of the seven churches of Asia in the order they were addressed in Revelation (see John and the Bishops of the Asian Churches), suggesting that this occurred after he wrote Revelation.
ii. Claiming Ambiguous Evidence
There has also been a tendency to claim for the late date a number of ambiguous passages as though the evidence were indisputable.
Origen and Clement
Origen’s reference to the “king of the Romans” who exiled John (Comm. Matt. 16.6) is often confidently claimed for the Domitianic dating, even though Origen does not identify the king in question.
Similarly, Clement of Alexandria’s reference to “the tyrant” after whose death John was restored from exile (Quis div. 42) is regularly claimed for the late date.
According to Clement, John settled in Ephesus after the tyrant’s death and traveled throughout the surrounding region, appointing bishops in the churches. This introduces the famous story of the baptism, fall, and restoration by John of a young man who became the leader of a group of bandits.
Interpreting Clement’s “tyrant” as Domitian is difficult to reconcile with the account for the following reasons:
i. it requires the unlikely compression of the account of the young man (his instruction, baptism, gradual fall, renunciation, formation of a robber band, final restoration) into the period of two or three years between the death of Domitian (96) and John’s death at the end of the first century.
ii. it requires holding that John didn’t travel through the province of Asia, appointing bishops, until this period of two or three years at the end of the first century, in his extreme old age. Why didn’t John ordain bishops in the earlier decades of his Asian ministry, as narrated in the Acts of John?
iii. it requires holding that Clement, who related that John ran after the young man while crying out to him, contradicted Jerome’s claim that John couldn’t walk and could barely talk in his extreme old age.
Irenaeus’s Ambiguous Statement
The famous passage of Irenaeus so often cited for the late date is usually understood to mean that the apocalyptic vision (not John) “was seen” (ἑωράθη) late in Domitian’s reign, but the verb “was seen” (ἑωράθη) is ambiguous (for more on this, see Eusebius’s Construction of the Domitianic Exile).
It can also be noted that the ancient Latin translator (translating likely a century before Eusebius wrote) did not understand the apocalyptic vision as the subject of the verb ἑωράθη, even though it is sometimes incorrectly claimed otherwise. This is because “apocalyptic vision” (apocalypsis) is feminine in Latin (and Greek), whereas the visum in the Latin “visum est” is either neuter nominative (agreeing with “the beast”) or a masculine subject accusative (agreeing with “John”) (see discussion here).
iii. Not Differentiating Victorinus and Eusebius
Thirdly, we can notice the indiscriminate appeal to both Victorinus and Eusebius for the Domitianic dating, without taking sufficient notice of their differences and their likely different chronological placement of the vision, that is, early (c. 85) and late (c. 96) in Domitian’s reign respectively.
It is seldom noted that Eusebius was the first extant writer to place John’s exile within the context of Domitian’s persecution of the distinguished citizens of Rome (Christian and non-Christian) in the 90s (an obviously unlikely setting).
While Victorinus does place John’s exile in Domitian’s reign, he does not specify when John was sent into exile. Victorinus could, theoretically, have placed John’s sentence as early as AD 81, and he does seem to indicate that he placed John’s sentence far earlier than Eusebius did, for he states:
There [i.e. Patmos], John seems to have written Revelation, and when, now an aged man [iam seniorem], he had thought that he would be able to be received [into glory] after his suffering, Domitian’s decrees were annulled after he was killed [AD 96].Comm. Apoc. 10.3 (my translation)
As Ellis notes, this seems to imply that John was on Patmos for many years, and that he suffered during this time in the mines, until at last, having grown old, he expected to be relieved of his suffering through death, late in Domitian’s reign.
The suffering which Victorinus mentions refers to John’s sentence “to the mines” (a claim accepted by few scholars). There is no evidence for mines on Patmos and Victorinus’s claim contradicts that of Tertullian, according to whom John was given the relatively light sentence of relegatio, which did not entail labor in mines.
iv. Citing Dependent Sources as Independent Ones
Lastly, sometimes writers are cited as evidence for the late date who were dependent upon Eusebius’s Church History for their dating of John’s exile (Jerome, Ambrosiaster, Severus, and, via Jerome, Bede).
These are obviously not independent witnesses for the late date.
See also the summary of my book’s chapter on the question: Patristic Evidence for the Early Dating of Revelation
References and sources mentioned in this post (except point iv) are discussed at length in Dean Furlong, The Identity of John the Evangelist: Revision and Reinterpretation in Early Christian Sources (Lanham: Fortress Academic, 2020).
 J. O. F. Murray, The Epistle of Paul the Apostle to the Ephesians, Cambridge Greek Testament for Schools and Colleges (Cambridge: Cambridge University Press, 1914), lxxxv n. 1.
 John Behr, The Paschal Gospel (Oxford: Oxford University Press, 2019), 67; Dean Furlong, The Identity of John the Evangelist: Revision and Reinterpretation in Early Christian Sources (Lanham: Fortress Academic, 2020), 109-110.
 Pieter J. Lalleman, The Acts of John: A Two-stage Initiation into Johannine Gnosticism (Leuven: Peeters, 1998), 16.
 G. K. Beale, The Book of Revelation: A Commentary on the Greek Text (NIGTC; Grand Rapids: Eerdmans, 1999), 20; Mark L. Hitchcock (“A Defense of the Domitianic Date of the Book of Revelation” (PhD diss, Dallas Theological Seminary, 2005), 26.
 E. Earle Ellis, The Making of the New Testament Documents (Leiden: Brill, 2002), 211.