I mark playlists "Make private". They do not revert to "Public" status. They are private but are showing up under my public playlists that other users see. On desktop mac and iPhone app. Other users on all devices see them.
If I understood you correctly, your private playlists also appear on your profile along with your public ones. You can easily take them off your profile from the mobile app by tapping and holding on the playlist > Remove from profile.
In case you meant something else, feel free to elaborate further so we can get a clear understanding of what you are referring to. You can also include a few screenshots which show how things look on your end.
Help others find this answer and click "Accept as Solution".
If you appreciate an answer, maybe give it a Like.