Technically, you're not supposed to be able to access the next stay's credits until all of the former stay's are used or expired. But we all know how "technology" goes at Disney. Your best bet is to get a paper receipt of what you have left on check-out morning so you at least have some kind of paper trail to back up any issues you may have.
ETA: ALL credits applies to your snack credits too, so if you were planning on using a QS credit from the second stay for a meal on transition day, that won't work if you still have snack credits to use from the first stay.