Yup, you shouldn't have moved the car. Maybe the driver thought that your signal is like an "it's fine" signal that is why he/she didn't go down anymore though he/she should have gone down. You should have chased that car.

That happened to me along EDSA Shaw. While I was waiting for the light to turn green, a car hit me and we both went down. At first look, we saw that his bumper went inside my bumper, just enough to make it bend. The light turned green so I said let's cross EDSA and bring our cars to the side as to let the traffic pass. Lo and behold, my bumper went back to its original state - self healed though it had some dents. I just shrugged it off and said nevermind.

The point is if he didn't go down from his car, I didn't move either. Nevermind if you're causing traffic, they could just go to another lane. You have to get the details first since once the driver runs, consider it done for you.