EDIT: Oh! Add GEICO to that! My son was not with Farmers when his accident occurred, he was with GEICO, and his went up.
Insurance is a risk based business. Low risk customers get better rates. Any indication of unsafe driving demonstrates you are a higher risk, so higher rates. Evidence of unsafe driving includes a history of at fault accidents and/or moving violations, either of which shows you as being a higher risk for a future accident.
Some insurance companies offer Accident Forgiveness auto insurance. Note that where it is available it is offered only for drivers with a good record or a fee.
If you are a long time customer with a significant history of no tickets or accidents, the first of either may be a freebie. Otherwise, be prepared to pay up. In either case, if you are a teenager or early 20’s, you likely do not have a long enough record for insurance companies to believe the absence of tickets or accidents so far is evidence you are low risk, just that you have not been caught yet.
Even longtime customers without tickets or crashes are not immune. My wife and I had been with Farmers for about 14 years when her collision happened - without any at-fault claims (though she had been struck two times in the previous dozen years), and we still saw that spike for 36 months. My son, well, he was 22.
Over the past 15 years I've had Mercury Insurance and Safeco. About ten years ago I got a citation in the middle of the night in the middle of the Mojave Dessert. I let it go on driving record with no increase of rate. My wife the same thing with a moving violation about 7 years ago. I was also hit in a parking lot and filed a comp claim. None of them did a thing to my rates. But I typically have no citations or accidents.
I have a group plan with two people and HO insurance. However, if we both got a point on our record, I'd expect an increase. But that is easy to avoid with TS.
again it is going to depend on many details (carrier, age, policy/combined, # cars, # drivers, state of DL/resident, state where you received the ticket, etc). Two people with a few instances and two carriers is in no way a big enough sample of knowledge to give any kind of reasonable answer to this statement :"No auto insurance company that I know of raises rates for the first moving violation or accident". Your key words are "that I know of".
That is your experience and others have had different experiences. Neither invalidates the other. It just means that blanket statements regarding how every agency will operate in every case cannot be accurately made.