Sometimes in World of Tanks on the Xbox 360 edition you get detected and an alert appears on the bottom of the screen. If you hide then the icon disappears.
You remain still some time visible to the enemies or you instantly disappear to their vision when this happens?
The alert just tells you that you've been spotted by an enemy tank. There is no event tied to when you are no longer spotted, so the icon disappearing does not mean you are no longer seen by the enemy.
However, the alert event trigger will reset if you are not spotted by the enemy for ~5 seconds, and trigger again next time you are spotted.
There are several factors that affect the time it takes to disappear, it's not worth it to calculate it exactly since it's different against different opponents.
My general rule of thumb is that when I'm spotted, don't panic... either move back into cover behind a solid structure or find a large enough bush and hide 20m+ behind it (you should reverse into this position so that the front of your tank is facing enemy for a better chance of bouncing their shots)
If I am spotted and I also spot the guy who spotted me, I will assume I'm also hidden (if I hide myself properly as mentioned above) when the guy I spotted disappears as well.
If I'm spotted but I don't spot anyone, then I would assume that I'm visible for 10s after I hide my tank.
Also note that once you think you're tank is hidden again, it's important to move from that spot and remain hidden. Unless that spot is a key point which you must hold or risk losing the match.
