I know out here on the West Coast weve got a few reverse credit states, where the non resident state gives the credit, instead of the resident state....not sure if other states have a similar deal or not.

Just VA and CA.

AZ and OR do it as well when CA is involved

No special form, just non resident return with explanation.

Should the client get a refund for the Local Taxes paid as well?

I don't think so. Maybe Daniel @Accountant-Man knows.

Check the locality website to see if they tax nonresidents.

Not for local taxes. In NJ, the credit for taxes paid to other "jurisdictions" includes local PA taxes, as well as of course Philly taxes.

NJ law doesn't say other "states" specifically so Philly wage tax and other earned income taxes are allowed.