Does Apple allow developers or testers to install previous versions of an App?

Solution 1:

No, this is not allowed. You can only have 1 version available for download in the App Store at a time for a specific iOS version (users with older versions of iOS can download the last compatible version of your app but I don't think that's what you're looking for).

I'm not sure if you can upload a lower version to TestFlight as I've never tried it. If it works, you can limit the ability to download it to specific users. That might achieve what you're looking for. Maybe someone can [edit] this answer if they know this is allowed.

Solution 2:

If you upload your builds to TestFlight, you can install older builds for testing.

When you open the TestFlight app, you’ll see the most recent version and a link to other versions. You can install any available version, but only one version at a time can be installed on a single device.

Note that TestFlight builds expire after 90 days, so this limits how useful it is to access old versions. You can re-upload older versions with a new build number to access them beyond 90 days, however you’ll have to take care to remember which versions correspond to which builds.