What does Acts 24:12 mean?

Paul is in Caesarea Maritima, on trial before Governor Felix. The high priest and some of the elders have just accused him of several things, including causing riots among Jews all over the Roman Empire. Paul points out that he's only been back for twelve days and he's spent five of those days in Caesarea (Acts 24:1–11). He arrived in Jerusalem to false rumors that he taught Jews they didn't have to circumcise their sons and spent much of his time trying to mitigate the damage and disprove the claims by fulfilling a Jewish custom to show his devotion to the Mosaic law (Acts 21:20–26). The only riot occurred when he was falsely accused of bringing a Gentile into the temple (Acts 21:27–31). Since Paul arrived in Jerusalem, he's done little besides defending himself against false accusations.

What Paul did manage to do was directly instigate a fight among the Sanhedrin. When he realized they weren't going to listen to his defense, he cried out, "Brothers, I am a Pharisee, a son of Pharisees. It is with respect to the hope and the resurrection of the dead that I am on trial" (Acts 23:6). Most of the Sanhedrin members were Sadducees who didn't believe the dead come back to life. Paul, and the Pharisees in the council, did. The Pharisees and Sadducees got into such an argument the Roman commander had to rescue Paul and take him back to the barracks (Acts 23:1–10).

So, the only "riot" Paul's accusers can accurately identify with Paul is the one that began because they, themselves, foolishly reacted to his words. As the proconsul of Achaia once determined, such disputes are "a matter of questions about words and names and [their] own law" and not the business of the Roman government (Acts 18:14–15).