The same situation could happen with a pedestrian walking in a crosswalk. A left-turning driver facing a circular green is watching oncoming traffic, sees a gap in the oncoming lane, accelerates, and then hits the brakes when he notices a pedestrian in the crosswalk. Or hits the pedestrian. The driver's error in this case is not confirming that both the travel lane and the crosswalk to be crossed will be clear of traffic.

It's unlikely that the driver entered the intersection lawfully on a green or yellow left-turn arrow, or he would have completed the turn through the intersection before your signal turned green. It sounds like he entered the intersection after your signal turned green. If his signal was red, he broke the law by running a red light. If his signal was circular green, he broke the law by failing to yield to through traffic before turning. You didn't cause the collision.