9/11 in NY being a classic example of how that isn't what people tend to do.
A wild disaster - terrorist attack - the likes of which none of those people would have ever witnessed before. A couple of the world's tallest buildings collapse. Thousands dead. The exact details of the circumstances mostly unknown, along with the continued risk.
The New Yorkers that had to evacuate the greater area, post attack and collapse, proceeded to overwhelmingly behave with great calm. They didn't trample each other to death. They didn't behave crazily. They walked out of there, peacefully, covered in collapsed building dust.
One of the many iconic photos of that relative calm behavior: