1) always call in insurance, regardless of who's at fault -in the case there is damage (to the riders or to the vehicles). They will take care of all the headaches, paperwork + disputes. ---and determines who was at fault
2) Even if the lady cut in, without any video proof, they can still argue that they turned in at last second of yellow light = they still had right of way (yes! even though your side already turned green).
You can ask Bangkok Metro for the camera footage from that intersection.
Again, if you called in insurance, you would not be doing all these
3) Even if your light turns green, ALWAYS be wary of this kind of accident. It happens all the time.