What happens when you get hit by an attack?
I don't think those visuals are physically painful; it's a psychosomatic reaction. The brain sees a bullet hitting your hand and responds as though a bullet actually hit your hand. Pain is at least partially neurological; you can feel pain even if your nerves don't fire.

Once the brain "checks" with the nerves in the affected area and realizes that the hand is okay, the phantom pain will subside, but in the meantime the lizard brain takes over.

I think that neatly ties into the themes of the show. The virtual world isn't just a fantasy realm with no actual impact on the real world; what you do there has actual consequences.