If I offer my defensive coordinater the head coach job (I had no head coach before this), and then offer one of my position coaches the defensive coordinater job, will both coaches just move up, or will the defensive coordinator be fired instead of promoted?
(I did both these offers before the countdown got to zero in the same day)

Both will move up

Thanks I wasn't sure.

On the transactions page, I think it will show that your DC was fired, but also show he was hired as HC, unless someone outbids you of course.

The only exception being, that coaches who are already employed can only sign one contract per season. If you just hired these guys, you may need to wait until next season to promote them. You could fire them, by hiring somebody else, but then every other player gets a crack at them.

Do it after EFA. :)