"I don't think you had to be from Rome to be considered a Roman"

This may be both true and untrue. One was generally considered part of the conquered province, then under control of Rome, but not Roman. However there were many paths to Roman citizenship, being born of Roman citizen parents, service to Rome, purchase of citizenship, etc. For instance the Judean Saul (later Paul, later St. Paul) held Roman citizenship, but was still a Judean. Jesus, a Judean in that Roman Province was neither a citizen of Rome nor Roman at all.

I have not studied general Roman History for nearly 50 years, so maybe someone else can expound on this more fully.