To elaborate on @rjs 's answer:
If you're a resident of NJ, then ALL your income is taxable by NJ, regardless of where you earned it.
If you're a resident of NJ who worked in DE, then your work income is also taxable by DE. If that's your situation, then you must file both a non-resident DE tax return and a home state NJ tax return. In that circumstance you would be able to claim a credit on your NJ return for the taxes paid to DE on the dollars taxed by both states, so that in effect you would not be double-taxed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
