Tacitus' reference to Christians in relation to Nero's persecution, including a reference to Jesus as the founder who was executed "by sentence of the procurator Pontius Pilate," has been widely discussed. Annals 15.44. Its authenticity is a settled question among academics and historians. Less well known, however, is a possible second reference to Christians by Tacitus. The gaps in the manuscript traditions leaves ample room for such a reference. The manuscript tradition for Annals is incomplete, ending around 66 AD -- well before resolution of the Jewish Revolt and the destruction of Jerusalem. Tacitus' Histories is likewise incomplete, ending in early 70 A.D. when it is believed to have recorded events through 96 A.D.
As is usual for ancient writings, fragments of Tacitus survive beyond and outside the manuscript tradition in secondary sources who cited his works, including Annals and Histories. One such fragment may be found in the writings of Sulpicius Severus, a Christian writer born in the mid-fourth century. His best known work is Chronicle or Sacred History, written in 403 A.D. According to Louis Feldman, "most scholars have . . . adopted the suggestion of Bernays that Sulpicius's source was none other than a lost portion of Tacitus' Histories." Feldman, Studies in Hellenistic Judaism, page 2. James D. Dunn suggests that the citation may come from the lost portion of Annals, noting that it "breaks off in book 16, when his account had reached the year 66, before the outbreak of the Jewish revolt." Beginning from Jerusalem, page 58, n. 25.
Here is the reference:
Titus is said, after calling a council, to have first deliberated whether he should destroy the temple, a structure of such extraordinary work. For it seemed good to some that a sacred edifice, distinguished above all human achievements, ought not to be destroyed, inasmuch as, if preserved, it would furnish an evidence of Roman moderation, but, if destroyed, would serve for a perpetual proof of Roman cruelty. But on the opposite side, others and Titus himself thought that the temple ought specially to be overthrown, in order that the religion of the Jews and of the Christians might more thoroughly be subverted; for that these religions, although contrary to each other, had nevertheless proceeded from the same authors; that the Christians had sprung up from among the Jews; and that, if the root were extirpated, the offshoot would speedily perish.2.30.6-7.
Severus notes that "it is said" ("it is reported" in other translations) by someone about the council involving Titus and the decision to destroy the Temple. This strongly suggests that Severus is relying on an earlier source. Although Severus does not identify the author of his source, this is not at all unusual for the time or genre. We know that Severus is otherwise familiar with Tacitus' Annals and quotes the passage referring to the Neronian persecution of Christians in the passage just prior to the one at issue (2.29). Notably, in the previous section Severus does not explicitly reference Tacitus as his source. So, there is no reason to expect him to have done so here.
Further, Severus relies elsewhere on Josephus but does not do so here. The passage at issue directly contradicts Josephus' account. Josephus reports that Titus opposed the destruction of the Temple. Severus' source reports that Titus supported the destruction of the Temple. Why divert from Josephus here unless he had good reason to do so? And if he was not relying on Josephus for his source then who? The inclusion of an account of the same council in Tacitus provides some reason for the departure, the fact that such an account refers to Christians whereas Josephus makes no such reference provides another. Moreover, Tacitus almost certainly wrote about the destruction of the Temple and had good sources for the period. Finally, a number of studies have shown that the language used by Severus in this passage is consistent with and may be indicative of Tacitus' style. (The first such study was by Jacob Bernays in 1861. More recently see Greek and Latin Authors on Jews and Judaism, Ed. M. Stern, Vol. 2, pages 64-67). For these kinds of reasons, most historians have concluded that the passage is indeed a fragment from Tacitus' lost writings.
I would add that the passage fits well with the historical context and Tacitus' earlier reference to Christians. Tacitus and other Romans were aware that Christianity had its origins in Judea and Judaism. But they also appear to have understood that Christianity was somehow different. Further, Tacitus and the Romans viewed Christianity with disfavor, even though it was "contrary" to Judaism, which was also often viewed with disfavor. These elements are found in the passage at issue: Titus knows that Christianity has its origins in Judaism but that the two religions by this time were in conflict. Obviously Christianity is viewed with disfavor as its destruction is a matter of state policy.
There is no suggestion in the passage that Christians are linked directly to the Jewish Revolt. Christianity is not just another sect within Judaism like the Zealots or the Pharisees, but another religion whose origins are Jewish but that is "contrary" to Judaism. Moreover, there is no suggestion that Titus believes that the destruction of the Temple will itself be a deathblow to Christianity. Although it would be going too far to credit Titus or other Roman officials with a sophisticated understanding of the differences between Christianity and Judaism at the time, they may have known that Christianity -- at least as known outside of Judea -- was not dependent on the Temple. The strategy seems to be that destroying the Temple will shatter Judaism and that, "if the root were extirpated, the offshoot would speedily perish." In any event, to the extent that Titus and the Romans had contact with Christianity in Judea, it is possible that -- consistent with the portrayal of the Jerusalem Church in Acts -- they learned that the Temple played some role in the lives of Jewish Christians in the area.