A message is considered processed for everyone when it has been read by a user AND assigned or responded to, OR when a message has been marked as "done".
If no assignment or editing has occurred yet, a red notification symbol appears next to the message, indicating that there might be further action required.
So, if you have read a message but haven't edited or assigned it, the message still appears as unread to other users.
The count of unread messages for a specific inbox or conversation is also displayed individually for each user with the red symbol.