It won't work that way for those two states because they have a reciprocal agreement. That means if you work in one state and work in the other, you only pay taxes for the state in which you live.
If you live in New Jersey and work in Pennsylvania, fill out Form REV-419 and give it to your employer. They should only withhold NJ tax.
If you live in Pennsylvania and work in New Jersey, fill out Form NJ-165 and give it to your employer. They should only withhold PA tax.
This year, you will need to first file a non-resident state return for the state in which you worked to get the tax you paid refunded. Next, you need to file a resident state return and pay the tax on your earnings.
https://ttlc.intuit.com/replies/4776822
