Puzzler with 2005 Tucson

I have a 2005 Tucson with 142,000 miles on it. It has been well maintained and runs great, most of the time. The most puzzling issue is that after I fill it up with gas, it takes 6-7 tries to get it started. This is the only time I have the problem. I have recently had the air flow sensor replaced since the check engine light came on and told the mechanic about the problem. He made a note to check the fuel pump. He also replaced the spark plugs and wires and said everything was in great shape. I went to the gas station and filled it, and the same exact problem. I took it back, he drove it and it ran great, which it does, except that now sometimes it acts like it’s going to die at a stop sign. I have run two containers of fuel additive that is supposed to clear out water in fuel or condensation and have changed gas stations-same exact problem, even worse. I am not touching the accelerator when I try to start the car. Since it does not show up on the computer diagnostic, no one seems to be able to figure out what the issue it. I am going to take my husband with me to fill it so he’s witness and video tape, because apparently if they can’t see it, they can’t figure it out. I am at my wit’s end and would love some suggestions to try.

It could be emission control related. Most cars have a valve that’s controlled by an electrical signal called a purge control solenoid. It may be stuck open so the fuel vapors flood the engine - iow, just too much gas present in the cylinders.
It usually is located on top of the engine but I’m not sure on your car. It is usually easily replaced.

What happens when you floor the accelerator pedal while starting it?
On an fuel injected car, that is one way to clear a flood condition as it stops the injectors from injecting fuel but runs the engine with spark.