State tax filing

Absolutely correct.  

Max allowed credit is the taxes that SC "kept"  (i.e. net after SC refund)

A second qualification of the amount, is that the credit allowed cannot exceed the % that NC would-have charged for the same income.  Thus, if the non-resident state taxes those wages at 6%, while NC taxes at 5%, then the credit is only for up-to the 5% that NC would have charged.

____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*