First, since there is a reciprocal agreement between NJ and PA, your PA employer should be withholding NJ taxes, not PA. This is the correct method and it will save you trouble at tax time - though if you are moving to PA to live in your new home, then its not necessary to correct this with your employer now.
When you fill out the Federal Personal Info section, it will ask for you resident state, which will be NJ. It will also ask if you made money in any other states. Since your employer withheld PA taxes, you will say "Yes and select PA". This will prompt the program to begin the PA and NJ returns, which is necessary because you will have to file both returns. This is all you will do for the states in the Federal section, but it is an important step.
When you are ready to do the state returns, make sure you do PA first. At this point, your refund meters will likely show you owing a large sum to NJ and getting no refund or small amount from PA. Go through the PA program until you get to a screen asking you to verify your income - see attached screenshots. This is the screen that you will need to tell the program that your wages are not actually taxable in PA. Select entire amount not taxable and finish the remainder of the PA program. Now, you should see a refund of your taxes from PA, but still an amount due from NJ (which is correct - basically you are going to have to pay NJ but get a refund from PA). Now, you can proceed through your NJ program like normal.
NOTE: If you worked in Philadelphia, then you will likely see a Philly Wage tax on your W2. Local taxes aren't included in the agreement, so you won't be able to get a direct refund of those taxes. However, you can include those taxes as an out of state tax paid to get a credit for them on your NJ tax return. There will be a question on this in the NJ program, so take your time through the program (see attached screenshots). You can include the local tax paid, but you cannot include the original PA state taxes from above because they are covered by the agreement, so be careful not to double add.
