My PA-based employer withheld NJ FLI, NJ SDI and NJ SUI (I'm a NJ resident). Do I need to file to get a refund?

The PA/NJ reciprocal agreement applies only to income tax - not these ancillary taxes.

My understanding is that since the employer is located in PA, they should have withheld these taxes for PA, because I am not eligible to receive these benefits from NJ.

If my understanding is correct, it would seem that I would need to get these withholdings back from NJ and pay PA.

How do I go about getting a refund and will I owe this money on my PA non-resident tax return?