You do not need to file a PA state or Philadelphia city tax return. NJ & PA are reciprocal. Your employer did it correctly, withholding NJ state tax but not PA (not withholding enough is a separate issue between you and your employer).
The reciprocal agreement does not cover city taxes. Philadelphia gets to take tax directly out of your pay. You cannot get it refunded. But you do not need to file a city return, unless there was a mistake in the amount withheld (unusual).
I'm not familiar with NJ forms. There may be a credit for the city tax withheld. If so, it will come up in the NJ interview.
