It is correct to pay state taxes in both. Your state of residence can tax all your income, regardless of where you earned it. A non-resident state can tax your earnings from physically working within its borders.
You can take a credit on your home state return for taxes paid to the other state, so you won't be double-taxed.
In TurboTax, complete your non-resident state return before you do your home state return, so that the credit flows properly.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
