I never once saw anyone run...
But I do recall people waiting inside before exiting and walking faster when it approached the time.
As a kid, living on bases...we ran! But if it started, we stopped. My dad was the XO, and having to face him because we were misbehaving during colors was not something I wanted to do.
He would not be amused, he was all Navy.
Nobody ran and certainly did stupid stuff like this. It tended to happen more in the peak of summer or when it was super cold.