How to enable automatic updates for alpha/beta testers at Google Play Store
I have configured the alpha/beta tests at the Google Play Store. New Google Group has been created for that purposes and required users were invited and joined the group.
When new update is available users have to go by the alpha/beta link to download and install the update. Is there any option to push update to alpha/beta testers (like prod Play Store works)?
Answer
I believe what is happening is that you did not send the "become a tester" link to your testers for them to click.
Apparently the part where you add the Google Group or Google+ Community to the Alpha/Beta testers on the Google Play Developers console you did all OK.
But also there on the console you'll get a link that is: https://play.google.com/apps/testing/<your app package name>
all those users/testers MUST click this link and click on the button "Become a tester" for it to work.
After that initial setup is done, your users should receive automatic updates just like normal production version.
hope it helps.