Don't worry about TX driving record. Any citation would be attached to the car and rental and not you since they can't prove who was driving at the time... and as you said the violation is not allowed per TX motor laws.

I wouldn't even worry about the CA intersection... as you said you saw a flash well after you were already out of the intersection. Those red light cameras take a picture of a vehicle as it is going through the intersection. Otherwise it doesn't mean crap if you're outside the intersection.