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No one said that Domitian did not persecute Christians, if tortures and banishings and the like counts as "persecution". There just is not any contemporaneous evidence of any actual martyrdoms under the much-exaggerated Domitianic persecution. (A persecution can be exaggerated by later writers, and still have been a hard time for those who were persecuted). Re-Read the quotation.

A good deal of the modern presumption in favor of a Domitianic date is based on the belief that a great, sustained period of persecution and slaughter of Christians was carried on under his rule. This belief, as cherished as it is, does not seem to be based on any hard evidence at all. While there is no doubt that Domitian was a cruel and wicked tyrant (I come to bury a myth about Caesar, not to praise him), until the fifth century there is no mention in any historian of a supposedly widespread persecution of Christians by his government. It is true that he did temporarily banish some Christians; but these were eventually recalled. Robinson remarks: “When this limited and selective purge, in which no Christian was for certain put to death, is compared with the massacre of Christians under Nero in what two early and entirely independent witnesses speak of as ‘immense multitudes,’ it is astonishing that commentators should have been led by Irenaeus, who himself does not even mention a persecution, to prefer a Domitianic context for the book of Revelation." (Chilton, Ibid.)

Fifth Century?

Eusebius, Ecclesiastical History
Book III, CHAPTER XVII
The Persecution under Domitian
Domitian, having shown great cruelty toward many, and having unjustly put to death no small number of well-born and notable men at Rome, and having without cause exiled and confiscated the property of a great many other illustrious men, finally became a successor of Nero in his hatred and enmity toward God. He was in fact the second that stirred up a persecution against us, although his father Vespasian had undertaken nothing prejudicial to us.
CHAPTER XVIII
The Apostle John and the Apocalypse
It is said that in this persecution the apostle and evangelist John, who was still alive, was condemned to dwell on the island of Patmos in consequence of his testimony to the divine word. Irenaeus, in the fifth book of his work Against Heresies, where he discusses the number of the name of Antichrist which is given in the so-called Apocalypse of John, speaks as follows concerning him: “If it were necessary for his name to be proclaimed openly at the present time, it would have been declared by him who saw the revelation. For it was seen not long ago, but almost in our own generation, at the end of the reign of Domitian.”
To such a degree, indeed, did the teaching of our faith flourish at that time that even those writers who were far from our religion did not hesitate to mention in their histories the persecution and the martyrdoms which took place during it. And they, indeed, accurately indicated the time. For they recorded that in the fifteenth year of Domitian Flavia Domitilla, daughter of a sister of Flavius Clement, who at that time was one of the consuls of Rome, was exiled with many others to the island of Pontia in consequence of testimony borne to Christ.
CHAPTER XIX
Domitian commands the Descendants of David to be slain
But when this same Domitian had commanded that the descendants of David should be slain, an ancient tradition says that some of the heretics brought accusation against the descendants of Jude (said to have been a brother of the Saviour according to the flesh), on the ground that they were of the lineage of David and were related to Christ himself. Hegesippus relates these facts in the following words.
CHAPTER XX
The Relatives of our Saviour
“Of the family of the Lord there were still living the grandchildren of Jude, who is said to have been the Lord's brother according to the flesh. Information was given that they belonged to the family of David, and they were brought to the Emperor Domitian by the Evocatus. For Domitian feared the coming of Christ as Herod also had feared it. And he asked them if they were descendants of David, and they confessed that they were. Then he asked them how much property they had, or how much money they owned. And both of them answered that they had only nine thousand denarii, half of which belonged to each of them; and this property did not consist of silver, but of a piece of land which contained only thirty-nine acres, and from which they raised their taxes and supported themselves by their own labor.”
Then they showed their hands, exhibiting the hardness of their bodies and the callousness produced upon their hands by continuous toil as evidence of their own labor. And when they were asked concerning Christ and his kingdom, of what sort it was and where and when it was to appear, they, answered that it was not a temporal nor an earthly kingdom, but a heavenly and angelic one, which would appear at the end of the world, when he should come in glory to judge the quick and the dead, and to give unto every one according to his works. Upon hearing this, Domitian did not pass judgment against them, but, despising them as of no account, he let them go, and by a decree put a stop to the persecution of the Church. But when they were released they ruled the churches because they were witnesses and were also relatives of the Lord. And peace being established, they lived until the time of Trajan. These things are related by Hegesippus.
Tertullian also has mentioned Domitian in the following words: “Domitian also, who possessed a share of Nero's cruelty, attempted once to do the same thing that the latter did. But because he had, I suppose, some intelligence, he very soon ceased, and even recalled those whom he had banished.” But after Domitian had reigned fifteen years, and Nerva had succeeded to the empire, the Roman Senate, according to the writers that record the history of those days, voted that Domitian's honors should be cancelled, and that those who had been unjustly banished should return to their homes and have their property restored to them. It was at this time that the apostle John returned from his banishment in the island and took up his abode at Ephesus, according to an ancient Christian tradition.

The Second Persecution - http://www.geocities.com/Athens/Ithaca/7730/Christian_martyrs/TenPers2.html

Eusebius wrote in the 4th Century, Tertullian in the 2nd and 3rd. Elsewhere Tertullian notes of the treatment meted out to St. John during his persecution:

Since, moreover, you are close upon Italy, you have Rome, from which there comes even into our own hands the very authority (of apostles themselves). How happy is its church, on which apostles poured forth all their doctrine along with their blood! where Peter endures a passion like his Lord's! where Paul wins his crown in a death like John's where the Apostle John was first plunged, unhurt, into boiling oil, and thence remitted to his island-exile! (The Prescription Against Heretics - http://www.newadvent.org/fathers/0311.htm, 36)

Tertullian's connection of the persecution of St. John with that of Sts. Peter and Paul is interesting (commemorated by the Roman Church festally on May 6 in the Feast of St. John before the Latin Gate), and strongly supports Tantumergo's claimfor the dating of the Apocalypse. If he was then freed circa AD 70 by Vespasian, we then have thirty years for St. John to busy himself with the Church in Asia and disciples like St. Polycarp and St. Ignatius of Antioch.

As to Domitian, if you had ever been to Rome, you can see the House Church of Titus Flavius Clemens, who Domitian executed for holding to "atheism and Jewish customs". It is two levels under the current Church of St. Clements. Pope St. Clement was a freed slave of the martyred Consul Clemens. Thus the Titula Clemens might be thought of as the first Vatican. It is quite believeable that the persecution of Domitian during his later reign was confused in some respects with persecutions during the time of Nero and afterwards (which might include Domitian's earlier reign), up to Vespasian, who ended them and successfully concluded the Jewish War.

However, you really need to stop using such easily discreditable sources.