First of all I bet you a dollar that YouTube video is edited to make the
effect look real or they are using one of the effects below and it only looks like the guy through something that explodes in
smoke.
Unless you have a huge budget, the best solution is to
call your local fire extinguisher/ industrial
safety/medical supplies store and rent a C02 fire extinguisher. Cheap and safe plus a great
effect.
There is a
Pyro solution. But the restrictions on
Pyro have increased significantly in the last 15 years. With the device I'm thinking of it's easy to get electrocuted if you do anything wrong, plus there is real flame on
stage. So you need to get proper training, get the thing approved by the fire marshall and your building authorities (school?). You may even need a
Pyro license depending on the state plus there are issues getting the device and materials in some states. No insult intended, but getting all those is unlikely if you don't currently have the knowledge to know what the device is called. This is NOT the kind of thing to ignore the warnings and do anyway as people can die.
So go with the C02 fire extinguisher. It's safe and spectacular. I used it for the beauty and the beast transformation a few years ago and it was perfect. I plan to use it for when Jonny comes back from the dead in Zombie Prom in a few weeks.
You could also use a well placed
fog machine hose. Note you can't control the time and amount of
smoke from the
Pyro solutions, but
fog machines and fire extinguishers are easy to control.