I forgot the type of car, but I have a 2001 Corolla that behaves exactly the same way. No mechanic has been able to tell me what the problem is. I have done a lot of experiments and it is definitely related to filling the tank. Here are some experiments:
1. Only let the tank go to 1/2 empty and fill the tank -> Result : No problem starting the car
2. Let the gas tank get down to 1/4 empty, fill the tank -> Result car is hard to start and runs roughly for about a minute.
3. Let the gas tank go to 1/4 full and add 1 gallon. --> result: No problem starting the car.
The on-board vapor recovery system is being over-loaded and floods the engine as you are refueling. The carbon canister is supposed to trap and retain these vapors, but on many cars, the amount of gasoline vapor exceeds the capacity of the canister the excess find their way into the engine. It takes a minute or two to burn them off…
Ray made mention of the purge system possibly being the problem and I though of the same thing when the question was asked. I would check the charcoal canister and see if it is flooded with fuel.
Due to the fuel venting systems todays fuel tanks are not meant to be topped off like you could do in ‘The Old Days’. Hopefully you don’t add extra fuel when the fuel nozzole shuts off automatically.