Thanks Roger, you beat me to the punch, and saved me a bunch of typing. LOL
I've heard and read many people say bass respond the pressure increase by moving deeper. If it were only the pressure delta which caused the move they would move shallower; by a few inches.
There is some other factor at work, and, as Raul said, nobody knows.
I do know, based on my experiences, that fishing deeper structure, using lighter line, lighter weights, and smaller, more realistic baits can sometimes be the ticket for post front conditions. Not always the case, but this approach works often enough to worth a shot. Why? I have no idea.