Generally, if a police officer is not at an intersection, it is difficult for them to cite a driver for running a red light (since they did not see the light). If the officer saw you run the light, or if there is other strong evidence from independent witnesses that you ran the red light, then you would clearly be the party most at fault.
Your question makes it pretty evident that you really don't know whether you ran the light or not ("I was in lala land"..."There is a possibility that I mistook the green turning light for my light") so it will be hard for you to defend a claim that you were at fault. It sounds like you placed the other driver into a sudden emergency situation and that he could not avoid the impast. I suspect that your insurance company will pay the claim and assess you with the fault for the crash.
Note that I am NOT an attorney in Washington, and it is possible that the laws are different in your state. But my comments are based on general law on the rules of the road that I believe would be true in most states.