Multi-state tax issue

I'm a resident of Alabama but work and live part-time in Tennessee.  My employer, who is located in South Carolina, is taking SC income taxes from my check. I asked that they take Alabama but for some reason, they don't think they can do so. I don't think I should be paying SC income taxes as I'm not working in SC. Am I right in thinking they shouldn't be taking SC taxes?  If so, is there something I can provide to my employer to have this changed?

 

Thanks so much.