My understanding with Kiffin is two things were going on at once.
A: Kiffin had already worn out his welcome at Alabama, he was gone after the season no matter what, whether or not he had a head coaching job. I can't verify this, but with all the Joey Freshwater stuff going around it's plausible.
B: Kiffin showed up unprepared and presumably hungover for the Washington game. He actually called plays the team had no practiced, which was one reason the offense was such a mess that game. This lead to his immediate removal instead of coaching the championship game.
This is all based on second hand information, but generally reliable. Kiffin just doesn't seem to do as well in the spotlight, Mississippi seems like a good place for him honestly, but don't get me wrong, I have him on my list just not at the top.
It feels like Lanning is out, but Saban also said he wasn't leaving.