I think your judgement was pretty good. The fire extinguisher probably would have extinguised the fire, then the latent heat in the car's metal would have re-ignited it. You could probably have gone through the cycle a few times until you exhausted the extinguisher, accomplishing very little and exposing yourself to real danger. Burning gasoline is very dangerous particularly in a pressurized tank. You said you assumed someone called the FD. I assume you called as well.

Tire fires are also quite dangereous and are also very difficult to extinguish, without a lot of water.

The outcome seems pretty good with no one hurt.

My first rule of responding to situations like this is to not multiply the danger for anyone by acting too quickly, without assessing the situation. Rule two is always call for help.