All new residents with out-of-state non-commercial driver's licenses must obtain a PA Driver's License within 60 days of establishing Pennsylvania residency.
All new residents are required to make application for Pennsylvania title and registration of their vehicle(s) within 20 days of establishing residency in Pennsylvania.
When you get pulled over, the cop is going to look at your license and ask, "Is this your current address?"
If you are working in PA during the day, and sleep in PA at night, you do not live in NJ with your parents.
EDIT TO ADD:
To be clear on this "new resident" status
61 PA Code § 101.1 "defines resident individual as An individual who is domiciled in this Commonwealth..." plus some exceptions that do not matter in this instance because OP is going to rent an apartment in PA.
Domicile is defined in the same section as "The place which an individual intends to be his permanent home and to which he intends to return whenever he may be absent."
Title 61 is the Revenue Title. So for tax purposes, you must have an abode and you must have intentions.
The Education Title (22) defines Domicile :
Domicile is the place where one intends to and does, in fact, permanently reside.
So for education purposes you must have intentions and your abode must be permanent. Having a drivers license is one form of proof of residency so presumably the driver's license residency requirement follows the Revenue definition!
Title 22 requires you to prove permanence, and 12 months residence prior to registration as a student is one factor. Oh, and Title 61 explicit tells us that you can be a resident for tax purposes but not for residency purposes.