I know that when a new version of an app is published to the Play Store, users do not all see it immediately. This is understandable; even Google probably doesn't want its servers being hammered when a popular app is updated.
I thought the delay was on the order of days, but now I suspect it's much longer than that. I turned off automatic updates because I like to be aware of when apps are updated in case a new bug is introduced. I check for updates every couple of days. It's not uncommon to see that an app was updated two or three weeks ago, when no such update was visible to me two days ago.
Can it really take three weeks for users to see updated versions of apps?