I'm not sure on how to stop the wetting through the pull-ups, but I can say that it's normal...completely.
My kids were such heavy sleepers, they wore them until at least age 8. All three - two boys and a girl. No matter how much liquid I would limit, or if they went to the bathroom right before bed.....wet at night. These kids slept through fire alarms, our house alarm - I'm sure they'd sleep through a tornado.
He will outgrow the night wetness sooner or later. No amount of bribing, pleading, etc will probably help. Just to put this out there.....I never made my kids help me change their sheets if we tried underwear at night, which we did. They cannot help it. They aren't playing some mind game or anything. Also, once they started overnights at friends houses, I made sure the mom knew , so that if my kid needed to be discreet, she was aware. It could be very embarrassing and luckily, my kid's friends were cool with it. I know some parents think that forcing the child to wet themselves at night in order to wake themselves to pee is the way to go. I, personally, do not believe in this approach. Sure, there could be some kids who are playing control games, but you'll know. This has been an issue for all my kids, so I guess it's close to my heart. Didn't mean to write a novel, here. LOL! Good luck!