Most Likely this is the law you broke.
http://www.azleg.gov/FormatDocument.asp?inDoc=/ars/28/00645.htm&Title=28&DocType=ARS
If this is the section of the AZ vehicle code you broke, you will see it is say as most state laws state about entering an intersection on green, yellow of red. It if the light is yellow it says you must be warned that it will turn red soon. It does not say anything about not entering on yellow. It also says if it is red you may not proceed pass the stop line or into a pedestrian cross walk. No where does it say if you're in the intersection and it turns red you violated the law. Also if the light complies with the MUTCD which all states are required to follow, there is condition called all red when all light in all directions are red for a period of time to allow cars to clear the intersection.
Also some state have laws about blocking an intersection which means you can not be in the intersection when it is red, and the other direction has green, this means you failed to clear the intersection during the all red interval.
The question you have to ask is was the light red at the time you cross the stop line, if it was and the front of the car was not passed the stop line or cross walk then you ran the red light, If you already pass those point you did not.
That is what the law says about running a red light. There is a few people here from AZ and they can tell you the specific about being served in AZ for automatic red light ticket if that is what you got. It is my understanding the ticket must be served in person since they have no other proof you were ever notified of the infraction.
