We've been having troubles preventing the popup from showing in our App Store app. The app is an Electron app, which means we're not using XCode to codesign it, but we've been able tyo get a normal (non App Store) signed version to work properly by using a requirements string. The app uses helper apps, and we've ensured that those are properly signed along with any relevant binaries. We used the com.apple.security.application-groups key and com.apple.security.inherit for child entitlements. And verified that these are being included properly.
Part of the problem is there doesn't seem to be a way to test this aspect before submitting to the App Store. We can't test apps signed with a distribution certificate, and apps signed with a developer certificate will always pop up the warning anyways.