You are correct to mark "No". New Jersey and Pennsylvania have a reciprocal agreement. As long as your PA employer withheld NJ taxes, you do not need to take further action.
If the employer withheld PA tax, file a Form REV-419 so they stop withholding PA tax. Next, in order to get a refund of Pennsylvania tax, file a non-resident PA tax return, reporting zero income as Pennsylvania sourced, and request a refund. For NJ, file a resident return and report the wages as if you earned them in NJ.
Here is more information on reciprocal states: What is a state reciprocal agreement?
