His language is completely pejorative, and while he gives the origin of the mname, what he doesn't do is to say how widespread it is, whether all groups of 'Christiani' are linked, or whether the name is used for unconnected groups which happen to use similar language. We might speak today of 'millennarians' who make the imminenent Second Coming a central plank of their religion, and say that the idea goes back to the person who started the Seventh Day Adventists. But the name encompasses numerous unconnected groups, some of which have very different agendas.
Writing at around the same time as
Tacitus, Pliny the Younger says of trials of Christiani that 'I do not know what are the cusomary penalties or investigations.... whether the name itself, even if inocent of crime, should be punished, or only the crimes attached to that name'. He questioned a number of former Christians, and discovered a harmless society, which they
had left when an edict against secret societies
had been published. He subsequently tortured two servant women, and discovered 'nothing but a depraved and extravagant superstition' (similar perjorative language to
Tacitus).
His concern isn't that he's dealing with a bunch or terrorists - he makes no mention of any such idea - but that there are allegations that the temples are deserted. It's an unlikely story on the
face of it, but similar allegations are a prominent
part of the story in Acts, written not too long before.
So there's clearly confusion about what these people are, what crime they've committed (if they were known to have torched
Rome, surely every governor would have known it!), and they're eventually banned under a general ordinance against societies, implying that at the time there was no specific law against them. I teach Religious Education, and I spend a great deal of time addressing confusion about Islam, which is far better known that Christianity was then; governments and police show similar confusion to my students. Just after 9/11, for instance, a local Sikh leader was arrested because a policeman saw a picture of Guru Nanak in
his house, and assumed that any guy with a long beard and a turban
had to be bin Laden! Given the prejdice displayed against the Christiani, which would have been exacerbated enormously if some of them were terrorists, I wouldn't trust the
Roman writers of the period to be at all objective about them.