If you make an app with existing installs private, then only the users on the private app list will be able to download that app from the moment you turn on privacy for that app forward. Existing installs will stay in place.
To restrict your app with existing downloads to ONLY the email addresses on your private app list, follow these steps:
Archive the app (this will erase all of the installs)
2. Re-activate the app from the archive
4. Resend out your install link to your users