tmux's extraneous visual bells in iTerm2

I recently started using tmux, I rely on visual bells (see Preferences -> Appearance -> Tabs -> Show new-output indicator) in iTerm2 to let me know when processes start/finish. When I start a tmux session in a tab of an iTerm2 window and then change focus, after a minute or two, the 'blue dot' appears in the tab. Nothing has happened in that window. I suspect that this is due to some behind the scenes activity (e.g. keeping the session alive?) Question : 1. How do I keep visual bells in iTerm2 while stopping tmux from issuing these extraneous bells?