I never do. I'm surprised how some fuel while still straddling the bike! I always turn it completely off and get off.Dunno about the US. In the UK you shouldn't be sitting on the bike when you're refuelling.
This time, doing same, standing and refueling, thing the tank was more empty than it actually was so didn't expect it was gonna fill up that fast. After it spilled, I capped it and got back on the bike and rode into the sunset