Yeah it seems to be the norm for universities in Florida. FSU has a police department that is an extension of the Tallahassee police department. My understanding is that FSUPD officers are TPD officers but work exclusively on the university campus. Their jurisdiction does extend outside the university grounds if needed but usually, they ask the TPD or the sheriff department to investigate off campus incidents.

It seems even the University of Miami (a private school) has a police force that is empowered by the local city.