I am a member of two Teams "organisations" . We have our own Teams setup for internal use and then I am also present as a guest in certain Teams/Channels in one of our client's Teams - for discussions around collaborative development project with the client. I get a switcher up next to my name (I am using Windows desktop client) which allows me to switch between the two.
This largely works. I think it's too slow and heavy when switching - seems to log me out and in to the other but it works to switch. The main problem is that it insists, most of the time, in showing a number of unread messages in the "other" team. I.e. currently if I am showing our Teams it shows 6 unread in the client Teams. If I switch it show 2 unread in our teams. I have nothing unread in either.
Frankly, this makes it almost worse to have the joint channel than not. I cannot keep switching (since it takes so long, and since I have work to do :)) so I have to rely on the notifications to know if there is something there I need to read.
Have had similar arrangements with clients using Slack which has worked really well...
I couldn't find a simple "Report a bug" location (which is, in and of itself, also a bug IMO!) so posting it here.
 not sure what the correct term is since a "team" is a sub-set within one such.
Good morning, I've experienced the same thing (when jumping between our own tenant and MSFT's). Not that is addresses the underlying issue, but I have found that clearing the Teams cache seems to remove the false notification.