ALL your income is taxable by your home state, regardless of where you earn it.
Other, non-resident states can tax you on income you earn from work that you actually (physically) perform within that state. There would be an exception if you're a W-2 employee and your home state has a reciprocal agreement with the non-resident state.
The employer's location is irrelevant. The issue is where you physically work. But if you physically go into the office once a week, the income from that work is taxable by the state where the office is located.
If you have to pay income tax to a non-resident state, your home state will ordinarily grant you an "other state credit" for all or part of those taxes. This effectively prevents double taxation.
If you tell us the states involved, we could give you a more specific answer.
Income is allocated to non-resident states according to the percentage of total income earned there.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
