NC does not tax non-residents who never physically work within NC. Nor are NC employers required to withhold NC state taxes from non-residents who never work in NC. See Nonresident employees on page 4 of the NC Employers Tax Guide:
https://www.ncdor.gov/media/13802/open
So if you were a full-year resident of TX and you performed no work inside NC, then your income is not taxed by NC. If your employer mistakenly withheld NC taxes, you can obtain a refund by filing a non-resident NC tax return on which you show the withholding but allocate zero income to NC.
The general rule for "sourcing" wages and personal services income is controlled by where the service is performed, not by the location of the employer. Otherwise (for example) everyone who works for Ford Motor Company would be paying income tax to the State of Michigan.
https://www.irs.gov/pub/int_practice_units/ftc_c_10_02_05.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
