How do tempura chefs touch 350 degree oil without being burned

As others have said, the issue is the hot oil and water interacting. You need to reduce or eliminate one in order to prevent the splatter or find a way to mitigate the damage.

Remember the basics - allow the meat to warm up to room temperature before cooking and pat it dry before you begin. That should allow you to use less oil without it turning into a charred lump with a raw center. You can use a lid or a screen to prevent splatter (you might need to adjust cooking time with a lid that will trap more heat).

I think you will find smoking inherent in the wok construction. Every bit of oil that spatters up the sides from deep-frying will smoke.

You may reduce smoking-sides somewhat by using the smallest burner possible but not entirely eliminate it. Many Chinese restaurant kitchens (many Indian too) have small 6 - 8" openings above furnace like flames that the woks nestle into. The sides are sealed against excessive heat.

Also, the heavier the wok the less the sides seem to start smoking ahead of the base which is counter-intuitive given the better distribution of heat by heavy or copper-bottomed woks. I am less certain about this point, merely personal observation.