Police pursuit into another jurisdiction over minor traffic offense - improper?

In NJ, I drove past a policeman who noticed my missing front license plate. I turned at the next road into another jurisdiction BEFORE he began any pursuit. He made the same turn and followed me 1/2 mile into another jurisdiction before putting his lights on and pulling me over issuing two minor non-moving tickets. I know about "hot pursuit" but this wasn't -- he hadn't even turned his lights on before I turned into the other jurisdiction and didn't do so until half a mile out of his. This just seems wrong to me.

If "another jurisdiction" was a different state or you were charged for violating a Hackensack city ordinance in Paramus for example, you might have an argument but local police are sworn to enforce New Jersey law throughout the state and the license plate law is a state law.