Yes that is true, and it should be within 5 minutes of your inavticity and right when you log-in or go to your page for the first time it might stay red for just a bit but just wait it out and it will turn green.
Oh and at the bottom of the community you can see users active in the last 5 minutes.
After about 10 minutes of inactivity, even if you still keep your browser open or don't log off, it'll turn red to signal your offline. And if you logout, it should turn red within a few minutes.
Green means your active, and you have did something in the past few minutes.