Apple native MusicApp on Mac redirects to web version of the service.
Apple music app installed on Mac, on Home screen after monthly replay is pressed opens web version of the app and asks for the iCloud credentials. It does on on the Mac, on every other devices the list of the most frequently played appears automatically. What's also funny on web site in the section "purchased" more the half items is missing and - once clicked, the purchased list appears on the Iphone.