Crews holding the car basically have to check. Failing to do so is called "unsafe release" and there is typically a penalty for that.

It isn't as chaotic as it looks. Going in the pit everybody is prepared and shouldn't be any problem. Going out there is a mechanic that signals when it's clear.

Sometimes there are screw ups, of course. Some bad and others quite funny, like when the driver stopped at his old team by mistake!