The white "frosting" that appears immediately after the the laser is water vapor, a byproduct of the laser tattoo removal treatment. Within 20 minutes, this fades and is not a burn or blister.
In the left hand is a hose that's connected to a cryo-chiller, a device that blows extremely cold air onto the skin before and during a treatment to help reduce any short-term swelling, a common side effect. It is not a vacuum.
What you see here was filmed in real time, showing just how fast tattoo removal treatments are.