Watched sessions display an "empty" play logo to indicate you've already seen them. If the play logo is still filled in, you haven't yet seen that session.
Watched indicators are at a user level (not cross-team) so you won't affect your co-worker's workflow if you were afraid of that.
In this screenshot, the green icons show sessions that are active and haven't been watched. The empty or white icon shows a session that has been watched. The blue icons show sessions that have not yet been watched.