Submit for SC W-4 to your employer and check box 7:
I claim exemption from withholding for 2021. Check the box for the exemption reason and write "exempt" on line 7. For tax year 2020, I had a right to a refund of all South Carolina Income Tax withheld because I had no tax
liability, and for tax year 2021. I expect a refund of all South Carolina Income Tax withheld because I expect
to have no tax liability.
You employer may not want to bother (and is not required to) withhold AL tax, but he should not be withholding SC tax, so that you don't have to file an SC return every year to get a refund. You'll have to make quarterly estimated payments to AL.
The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.
Since TN does not have an income tax, you do not have a non-resident return to file. But you still have to pay tax on that income to your home state (AL). In other words, having worked in a state without an income tax does not get you out of paying state tax on that income, to your home state.
You say "I'm a resident of Alabama". That means you owe AL tax on all your income. Working and living part-time (I assume for work purposes) in Tennessee, does not get you out of that. If your work state was one with an income tax, "live part time in TN", might get a little trickier, but almost always comes down to pay tax to the work state and home state take a credit from the home state.
