Which state is Out Here? Only OH, OK and OR are in the 50.
Inside Philly and the PA suburbs mean PA 40. Is Out Here also PA? Then NJ should have never been withheld. Then PA is owed all 3.07% tax on PA wages(not necessarily the same as Philly wages) and she gets back all NJ tax assuming she never lived there.
The reciprocal agreement only works for NJ residents working anywhere in PA or PA residents working in NJ.