I can see from my iTunes connect control panel how many users are on each version of the app I have in beta. When does TestFlight update those apps? Do they have to open TestFlight and manually choose to update? Does it happen automatically when they launch the app they are testing?
I can't seem to find any answer on Apple's documentation.
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It might be possible to do a force upgrade, see https://stackoverflow.com/a/12319198/330067, however I didn't find any details so far.
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As of November 11, 2020, TestFlight version 3.0 now supports automatic updates:
Source: https://www.macrumors.com/2020/11/11/testflight-app-automatic-update/
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After a while, I found a solution that works every time.
You need to remove the version from testing by selecting Not Available for Testing. Then save, approve and reselect the version you want to test and save again.
This will make all your TestFlight users receive a notification with the update (event if they have a different version installed).
They have to manually update it. A push notification and email is sent to let the user know that a new version is ready to be tested, but it's up to user to open test flight and install it.