Your accountant is referring to "reciprocal" states. But New Jersey and North Carolina do not have such an agreement. Look up "tax reciprocal states" and see what you find.
Note that the entries for state withholding on your W-2 is just a statement by your employer of what they did and which states they sent the money to. it does NOT mean that your employer did it right (or even knew what to do).
In most cases, you are taxed in the state where you live and in the states where you work.
For example, your employer may not be able (or willing) to do state withholding for North Carolina (it involves creating an account with the state and sending the money and reports there).
In TurboTax, you should enter your New Jersey data first as a non-resident return, then enter your North Carolina data as a resident return. In this case, states either allocate income to the two states, or they use the taxes paid in the non-resident state as a credit in the resident state. It will work out so that you are not double-taxed (much).
And do talk to HR or payroll and see is you can get them to do real withholding for North Carolina.
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