You said you work remotely "in" New Jersey. Income from work you actually (physically) perform within NJ is fully taxable by NJ.
But if you never physically work within NJ, then your work income is not taxable by NJ, and your employer should not be withholding NJ taxes. In this situation, if your employer did withhold NJ taxes incorrectly, your remedy is to file a non-resident NJ return, on which you show the withholding but on which you allocate ZERO NJ income. In this situation you would NOT claim an "other state credit" on your MA return, because in fact you would owe zero taxes to NJ.
Work income is "sourced" where the work is physically performed. NJ can only tax non-residents on NJ-sourced income. The work income of a taxpayer who works solely from an MA location is MA-sourced, not NJ-sourced. The employer's location does not determine sourcing.
But if you did do some work in NJ and you do owe NJ tax, then you would claim an "other state credit" on your MA return for the taxes paid to NJ. The "other state credit" is granted by the taxpayer's resident state, not by the non-resident state. The NJ tax person you spoke to was completely incorrect in this regard.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
