Individual Income Tax Adjustment
Well, it seems from what you have described that when you moved to PA you were working in NJ and hence the W-2 you received sourced the Wages to NJ. This is correct!
I am trying to understand how your tax return was filed incorrectly, as NJ taxes the entire income earned in NJ State for a part year NJ resident. This amount is reflected on the W-2 for NJ State.
Unless of course you did not file an NJ state tax return and included the entire income in PA State. In that case, it is relatively simple, you have your CPA file an amended PA tax return and file a NJ State tax return and pay the taxes applicable to NJ State on the NJ income earned through the W-2. As for the PA amended State tax return, you will get a refund as the income was earned in NJ.
On the Federal income tax return, there are no changes to be made as the Federal income tax return will be unchanged as you have reported all the earned income as reported on the W-2, and taken the appropriate deductions for the state income tax withheld on the W-2.
Hopefully, this should help you, and if there is something I have missed please let me know.