Isn't that so that to get the shops open, the owner actually has to unlock those doors? Because IIRC, it's stated in the mod's readme that when using the immersive waiting feature, the AI may get off the schedule. However, it should solve itself when you give them an hour or so. I am using this mod without any damaging problems...
EDIT: Time Manager sets the speed of the NPCs up to compensate for the high timescale, but it is still possible that they just cannot keep up. The longer you wait, the bigger the deficit. Eventually, they will get synced again.