If Saban wanted him gone, he would have told Tommy Rees that he wasn't going to retain him. A playoff appearance basically means that he gets at least another year.
Saban doesn't beat around the bush when it comes down to that kind of thing. If he wants someone gone, he'll send him on his way. After all, he sent Bill O'Brien packing in late December of 2022.
Furthermore, Tommy Rees would be foolish to leave Alabama right now. He took a good step forward in terms of learning how to actually be an OC, even if he did regress a bit at the end of the bowl game.