Here at The Zebra we work with many different insurance carriers depending on your state. Not only do we work with carriers that are lesser known, but also some of the bigger name companies such as Progressive, Safe Auto and Travelers.
It depends on the exact rules for California and laws do vary state to state, but for the most part if your license is valid and you transfer to a new state insurance companies won't see prior activity. They will run an MVR for CA and only show info that is on that license.
If your insurance company has deemed your vehicle to be a total loss, you can expect them to pay you the actual cash value of your car minus your deductible. See more about total losses in car insurance here.