It works like this:
PA non-residents who work in Philadelphia are subject to the Philadelphia wage tax.
Income you earn from work actually (physically) performed within PA is subject to PA state income tax.
ALL your income is subject to DE state income tax, regardless of where you earn it.
You'll be able to claim a credit on your DE tax return for the state income tax you pay to PA (although the credit cannot lower your DE tax below zero - it is not a refundable credit). DE will not allow a credit for the Philadelphia wage tax.
So at year's end you'll be liable for:
100% of the Philadelphia wage tax
100% of the PA state income tax
100% of the DE state income tax, less the credit allowed for PA state income tax
DE has a graduated income tax rate from 2.2 to 6.6%. PA has a fixed rate of 3.07%. So you are likely to have a DE tax bill even after applying the credit. Therefore I think your employer is withholding correctly.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
