Simply describe the symptoms to the mechanic.
If he is worth his salt, he will know what to look for.
In case his eyes glaze over when you describe the problem, you might want to say that you have been told that the problem could lie in the evaporative emissions system.
If it turns out that my diagnosis is correct, I hope that you realize that you really shot yourself in the foot with that click-click-click routine. Unless you are about to drive across the Gobi Desert, there are more than enough gas stations around so that you don't have to worry about being able to drive--perhaps--five miles further before the tank is empty.
On Toyotas, replacing the carbon canister runs ~$300--or more, but I have no idea of what it might cost on the Aveo. Hopefully, it will be less.
Even if you don't need to have the carbon canister replaced, do yourself a favor and stop filling the tank when the pump clicks off for the first time. The Chevy Aveo has a pretty poor reliability record, and doing things like you have been doing will definitely not help the car.