To use your hypothetical scenario:
If you become a MT resident on 1/1/2023, then at year's end you will file a resident MT tax return. If your employer does not withhold MT income taxes for you in 2023, then you must make quarterly estimated tax payments to MT during the year. Once you become an MT resident all your income becomes taxable by MT.
If, after your move (and assuming you never work in NC in 2023), your employer incorrectly continues to withhold NC taxes, then at year's end you'll have to file a non-resident NC tax return, on which you report the withholding but declare zero NC income. This will result in NC refunding the incorrectly withheld taxes to you.
Your residency for tax purposes is not determined by the address you put on your tax return. It is determined by the actual facts and circumstances of your situation. The address on your tax return simply tells the taxing authority the address they should use in case they need to contact you.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
