What they are doing in the video is heating up the liquid inside the vessel, (with an open lid).
Then they take it out and immediately (i.e. before it cools down), they pack the lid.
What happens is that as the liquid cools down, and the temperature (in Kelvin) drops then the pressure drops. An approximation is the ideal gas law (although as Abel pointed in ...
Not checked out the video, but if you put a jar with a liftable lid in a vacuum sealer then as the pressure outside the jar is reduced air in the jar will push past the seal to equalize the pressure.
Once the sealer is opened then as long as the jar seal is good the reduced pressure will stay in the jar.
They heat the jars and take them out of the oven open the lid to let the pressure out and then close it.
Once the jar gets cooler the pressure inside that was occupied with hot expanded air settles and the air volume shrinks back causing it to create a small vacuum.
Many times early in the chill mornings I see my bottle of water left in the cup holder ...