State Tax vs No State Tax

 Q. I was paid some of this Florida income  after moving to SC.  Am I required to pay and file a state return anyway?

A. Yes. All income received while you were an SC resident, is taxable by SC, regardless of where the income was sourced. 

If you had been taxed by FL, SC would give you a credit for FL tax paid. 

When you worked in a state without an income tax (e.g. Texas or Florida), there will be no credit, since there was no FL tax. In other words, having worked or other income sourced in a state without an income tax does not get you out of paying state tax on that income, to your home state.