Dynamic Groups - Auto update??

Summary

Are dynamic groups supposed to auto update when user criteria changes?

Content

We use dynamic groups. It was our understanding if we set dynamic criteria for the groups that as an user's data relevant to the dynamic criteria changed, so would their membership in the group.  For example, when your account was initially created you did not have a supervisor role but later your account was updated to include one, they dynamic group whose criteria is based upon having a supervisor role would update to include you.  Is that a correct understanding of the functionality?  If so, it is NOT working for us, at least not 100% working.  Anyone else experience this?