According to the following FAQ, the Alabama DOR says "Please allow 8 to 12 weeks to receive your refund."
Also, as a fraud prevention measure, some Alabama state refunds will come by check even if direct deposit was chosen.
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-alabama-tax-refund/00/26558
But there are some things you need to check.
First, if you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking in your Online account at the Tax Home.
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
The FAQ below tells how to check on a state refund and has a link for your state.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571