I think I inadvertently caused an accident.

It happened here. I was going south on the MUP. The MUP on the left side has a pedestrian light, which I always press if I get to the intersection during a red light. So I wait to get the signal, and of course during rush hour there are always a bunch of people turning after the green left turn light switched. By that time (having a green light I am on my way across the intersection) some guy still tries to make the left turn, I suppose he saw me, and slowed down. And thats when he got hit by an oncoming car. The left turner barely moved and the oncoming car slowed down enough so that the accident wasn't bad, but still both car were damaged.

I somewhat feel bad, but I really don't know what else to do. There are always stragglers that will try to run the light in the last second, I am already trying to navigate the the right turners that come from the other side (who may or may not respect my right of way).