My team uses TestFlight to deploy beta builds within the company. Frequently, the TestFlight App does not want to install the latest version.
For example, we will get a TestFlight email informing us about an App update for build #91. The email includes a link ""Open in TestFlight". When you tap the link, TestFlight opens, but offers to install build #90 (an older build), instead of build #91 (the latest).
In the "Prereleases" list for your App, once your build has finished processing, you'll be able to click the link for that particular test build and go a page with meta data about it. Switch to the "Test Information" tab.
I had filled "TestFlight Beta Information" section, but empty "Beta App Review Information". After filled second one and saved, I received email and notification about new build available.
Fill whole form :P