Locally "jumping" a light has a specific meaning, meaning starting before the light changes, as in jumping the gun. So it's different that someone crossing mid cycle (if/when there's no cross traffic).

Around here, and especially where I worked the lights had little meaning. A green offered little protection because the number of red light runners (cars) was too high, so I treated ALL intersections as if they were unregulated and went when it was safe regardless of the light.

One little irony would be when I'd roll up to a red where a police car was stopped. I'd stop alongside, and often the officer would roll down the window and ask me why I was waiting.