How soon will wet tail symptoms in hamsters appear?

I have two robo dwarf hamsters that live in the same cage. I noticed the matted fur on the tail of one of them, and took him to the vet. The vet verified that he was ill and is keeping him overnight for a few days, but he also said to look out for my other hamster. How soon after their last interaction will I know if my other hamster is infected as well?
Answers

Quetzel

Unless they are kept in very dirty, poor, crowded conditions, it's not too likely it's wet tail. If your second hamster doesn't have diarrhea now, it probably won't.