What does it matter if there are not?
Answer: it does not matter for our purposes. the discussion here is about Christians in Rome, which were 1. an identifiable sect; 2. strongly disliked by the literary elite; and that there was a connection between the sect in Rome and events that took place in Judea under Pilate
Actually it does matter because we do not know where Tacitus got his information. The only other non Christian contemporary to Tacitus to mention Christians is Suetonius and he simply says Nero "punished" them. Why is not stated and from the order Suetonius puts events in it appears this occurred long before the fire. More over neither Josephus or Pliny the Elder who were in Rome 64 CE mention Christians at all.
In fact, as related by Origen the siege of Jerusalem began during Nero's reign and one can see the Emperor wanting to stomp any idea that a Messiah (or in Greek Christ) would do a Moses and liberate the Jewish people.
As recounted by Josephus this Messiah concept had been a minor headache for Rome near on 70 years with Simon of Peraea (d 4 BCE) being the first major figure. But by 66 CE the situation had resulted in full rebellion in a part of the Empire and that was something Rome did not tolerate.
But was Nero going after Christians as we use the word (ie followers of Jesus) or was he going after various sect that believed in a Moses like liberation via a Messiah (ie Christ) given the meltdown in Jerusalem and Christians of the 2nd century later claimed these people are part of their sect? We don't know.