When you file your income taxes next year, you will file a return for South Carolina and a return for Alabama. Tennessee does not have state income tax.
You will show that you paid taxes to South Carolina and assign those taxes back to Alabama. When it asks what percentage of the income was earned in South Carolina, you will put zero. You will then put 100% for Alabama on the Alabama return.
Just remember to do your non-resident state first. That way TurboTax will compute this correctly.
You are correct that your employer should be withholding taxes for Alabama. If they make that correction, you will not have to file two state returns in future years.
The law is that you cannot be forced to pay more than one state for the same income. No double taxation is allowed.
