How long does it take for a new version of an app to reach users? 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?
I guess it depends on how the developer targets the audience .  If the developer chooses to do a staged rollout 


  You can release an app update to production using a staged rollout. With a staged rollout, your update reaches only a percentage of your users, which you can increase over time.


(Emphasis Supplied)

For more details see the link

It's best to contact the developer and check