Question

When a state exercises jurisdiction over property within that state, this type of jurisdiction is called in personam?

Answer 1

That statement is false.
Personam refers to a situation when the States exercise jurisdiction over DEFENDANT within that state.
If for example, the defendant conducted their accused crime on the State of California, the state of Arizona couldn't possess the right to try the case in Arizona.

Answer 2

It is false that this kind of jurisdiction that state exercising the jurisdiction over property in state is Personam. Personam is more of a thing that is regarding one single person. It's like if a case is against the particular person then the respective summons and whatever the complaints are served only to that individual and the judgement is also only on him.