No, you will not need to do this. If NJ taxes were not withheld from your check, you will not need to file a return for NJ because PA and NJ are reciprocal states that agree that you are only taxed on your wages to the state where you live, and not where you work. Therefore, if you did not have NJ state taxes withheld, you may delete the state return. Here is how you would do that: https://ttlc.intuit.com/replies/3301384
Even if NJ taxes are withheld (mistakenly), you still will not need to enter the adjustments. You will adjust your income in NJ to show zero income, and that way you will get back all of the NJ state taxes withheld from your paycheck (which you will pay to PA). You will also want to file a form with your employer so that they withhold PA tax instead of NJ tax. Here is an FAQ to assist you with this: https://ttlc.intuit.com/replies/4776822
Finally, here are some screenshots from the NJ return so that the income is exempted because of the reciprocal agreement with PA:
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