Here's how it works:
Your home state of NY can tax all your income, regardless of where you earn it.
NJ can tax any income you earn from work actually (physically) performed in NJ.
Therefore you should have filed a non-resident NJ return and your home state NY return.
On your NY return, you'll be able to claim a credit for the taxes paid to NJ, so in effect you won't be double-taxed.
Important: In TurboTax, you must complete the non-resident NJ return first, before you do the home state NY return, so that the program can calculate and apply the credit correctly. I suspect this is where you made your mistake.
If done correctly, the majority of your state tax bill will be due to NJ.
You may have to file amended returns to correct the situation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
