I used to mod two pretty large subs (iirc something like a combined ~400k subscribers) and we had no way to detect ban evasion other than the user being stupid and obviously giving themselves away (eg. “fuck you mods, I’ll just keep making new accounts”). This was fairly recently and I left the site and quit modding about a month after they pulled the API bullshit and booted Apollo and other apps.
So unless reddit added additional tools for mods, your story doesn’t quite add up here.
Ah yeah that’s not a mod action. That’s a Reddit site-wide thing on the admin side of things or some automated system they have. Subreddit mods had nothing to do with that.