What causes the bucket to launch in the air?
Unusually for an exploding-potassium demonstration, this one uses a potassium sample attached to a weight. This causes the potassium to sink to the bottom of the bucket, where it generates and ignites hydrogen gas. This creates a temporary bubble launching the water upwards and the bucket downwards. The bucket's motion gets blocked by the table, but the water is free to rise. The bubble quickly cools and collapses, and air pressure pushes the bucket upwards towards the rising water.
It does press hard on the table surface. There are two possibilities here.
If you watch closely, it almost appears like the bench has a spring loaded mechanism which gives the container a rapid lift at the point of the reaction. This is could have been done for “theatrical effect”.
Another possibility (and more likely) is that when the reaction takes place, the rapid ejection of gas and chemicals upwards will cause the container to press downward causing a depression in the surface of the table. Then very quickly the table then retains its original form (think about compressing a spring then letting it go) and causes the container to rise rapidly.
But you were correct to point out that it makes no sense for the container to shoot directly upward as if the reaction provides some form of vertical thrust, which it obviously should not given that the chemicals themselves shoot upwards and not downwards.
Edit: It has been pointed out in comments by others who slowed the video down to a frame/second and pointed out that the surface of the bench remains deformed for a short time after the container leaves the bench.
Another possibility (perhaps the best) is that as the reaction happens, this caused the sides and bottom of the container to expand rapidly. The outward bulge therefore on the bottom of the container caused by the rapid expansion of chemicals and gases, causes it to launch itself because this expanding bulge pushes off from the surface of the bench.
I am not particularly satisfied with the answer of Dr jh.
the table is still deformed downward when the bucket is lifted off of the table. there is a coaster(?) on the table that the table has been pushed below, but has yet to rise back to push it up, and, when it does, the item while much less massive than the bucket of water is not launched as high.
the explosion pushes water away from its source. this force also pushes against the table, but because the table is solid and attached to the earth it does not move (much) and instead accelerated the bucket up.
If a spring is compressed into a table then released, the spring expands about its center of mass putting force into the table. Since the table doesn't move, the spring rises from the table. The same thing is happening here.