If you were caught running a red light by a camera this is normally referred to as a red light camera ticket. In this type of situation you are flashed by a camera for entering an intersection after your light has turned red and you then receive the citation in the mail for this offense. This ticket is not automatically sent to the vehicle's insurance carrier.
If you pay the fine for the ticket, and thus are convicted of the offense, then depending upon your state's laws the violation could go on your driving record and thus affect your insurance rates. It does not mean an automatic rate increase for this one ticket. It will depend upon your overall driving record and the rating system of your insurance company to determine if this running a red light offense will change your car insurance premiums.
Insurance companies usually do a policy review every 12, 24, 0r 36 months and re-evaluate your driving record and rates.
So it will depend upon state laws as well as your insurance company's rating system if a red light photo ticket will affect your insurance premiums. For instance in some states a red light ticket is not placed on your motor vehicle record (MVR) then your insurance company would not normally know about it and thus it could not affect your rates.
For example, Maryland has red light cameras that allow for photos to be taken of those entering an intersection after the light has turned red and thus sends them a citation. However, according to the Maryland District Courts site, payment of the penalty for this type of violation does not result in MD points being assessed to your driving record and cannot be used to increase your insurance rates. It is basically handled as a parking ticket.
So if your ticket and license are in Maryland your insurance rates should not be affected if you took responsibility for the red light photo ticket.
On the flip side are states like California and Hawaii consider a red light photo ticket to be a moving violation, just like a normal running a red light ticket given to you in person by a police officer. If you are convicted of a red light camera ticket in California your driving record will be assessed one point and your insurance company can rate you on this offense.
The Hawaii DOT notes that it is up to your insurance company and how they determine your policy rate to determine if your rates would rise due to a red light camera traffic ticket.
So to find out if your rates will rise due to a red light photo ticket in your name, check first with your state's Department of Motor Vehicles to see how the ticket classified. If it is a moving violation, just like a normal running a red light citation, and thus placed on your MVR then you will need to check with your insurance company to if according to their rating system your rates will be raised.