Usually, the browser tab helpfully tells you who’s move it is. This is an important way to know you need to come back from surfing cats (or studying tsumego) in order to play your turn.
However, if you do some analysis using the analuze tool, and don’t click “Back to game” before going off study tsumego, the browser tab stays on “Black to move” (if you are white) and doesn’t change back when your opponent moves !
This is most applicable in correspondence style games, where you are actually likely to look at something else when it’s not your turn. In these games time is not so much of a factor, but it’s still a bit of a nuisance to lose that notification.