Chuck, this is a most profound question about one of my favorite stories.
It warms my heart that a Roman Centurion would love and respect Jesus as much as this.
About your question, I can only guess.
Could it be that even though Herod Antipas ruled, Rome felt the obligation to "assist?" Herod Antipas could have complained, but it is doubtful such complaints would've been given much weight.
Or could it be that, though the Centurion lived here, he was stationed elsewhere. This, of course, seems less likely. The commute to work wouldn't have been as easy or swift as it is these days.
Or perhaps the status of Herod Antipas wasn't that of absolute ruler of the region on behalf of Rome, but merely an administrative role with no "policing" responsibilities.
I wish you luck finding the true answer.