As to a citation - well you have been rather grandly posturing about your expertise in Tacitus to St Frank, but apparently have not read it. Tacitus, volume 3 book XVI specifically refers to Nero's spies.
So first you refer to my ignorance of Tacitus by referring to a "volume 3 book xvi" that doesn't exist except in collections of the entire works of Tacitus which he never produced. Then you tell me I am not familiar with Tacitus' book Annales, chapter XVI, because you read some translation you came across which was poorly translated. There is no word for "spy" in Latin, and in general Tacitus describes Nero's use of his soldiers and guards using metaphors:
"In Tiberius' day, informers might be said to have been actors in that they gave false testimony (e.g., 4.36.3); In Nero's, however, genuine actors, such as Paris, are informers, and the charges they bring are just as false. Woodman has demonstrated hos Tacitus relates the Pisonian conspiracy with a mixed proliferation of theatrical imagery and terminology. Similar figures of speech are evident throughout the reign of Nero. For instance, when the emperor's conspirators trump up charges against Agrippina, Tacitus portrays them in theatrical terms..."
L'hoir, F. S. (2006). Tragedy, rhetoric, and the historiography of Tacitus' Annales. University of Michigan Press.
I can't be sure what translation you relied on, but some internet searching for free English translations revealed some which, in book XVI, chapter 5, of Annales, use the word "spies":
"For it was a graver ground of fear to be missing from the spectacle, since there was a host of spies openly present, and more in hiding, to note the names and faces, the gaiety and gloom, of the assembly." (source)
There is no word here that is translated as spies. The Latin refers to "multis palam et pluribus occultis" ("many known and more hiding") who were among the spectators of Nero's public performance so that the nomina ac vultus ("names and faces) of those who weren't adequately laudatory and receptive scrutarentur ("were carefully noted").
In other translations sometimes the spread of rumors about Nero by his personal security apparently made the translator decide that "spies" was best used to translate "bodyguards". Tacitus uses this same word to refer to the public stationing of soldiers/guards whose duty was also to note what they saw/heard just like modern security guards.
Most importantly, a translation I found that uses "spy" to describe Nero's own bodyguards who spread rumors about him are able to do so because he was an idiot who couldn't help but make a fool of himself. You're suggesting that because you read some translation of a language you can't read that describes informants, plots, and so forth in Rome means that Nero had some sort of network that informed him of a marginal and marginalized movement not yet really distinguished from the Jewish matrix it grew out of despite the fact that
1) Years later, Pliny's letters indicate both Trajan and Pliny didn't know what to make of these weird atheists who refused to practice the least required by religio-political law, but Nero was on the ball with his "intelligence agency"
2) That multiple emperors had consistently failed to predict massive revolts despite their "intelligence agencies" even after Roman governors we installed (and fired for ineptitude) to keep a closer eye on Jerusalem, but Nero was sufficiently informed about a particular "Jewish" sect/movement because of "spies".
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3) Finally, that Nero's knowledge isn't far more easily explained by the infamy (and to a much lesser extent acceptance) of Christians thanks to the fact that unlike the "Hebrews/Jews" they were both proselytizers and sought to convert gentiles, unlike Jews, but whose religion was just as alien and in violation of law. Only Nero couldn't make scapegoats out of Christians if nobody knew who they were.