Q: Why does the water in one column move into the other column?
A: Your kit will produce a difference in water level in the two columns of the airlock.
Here is what is happening:
When the jar is charged with salt, water, and then vegetables are added; spontaneous fermentation begins. The concentration of mineral ions in the brine is greater than in the liquid within plant cells, which causes the cellular plant fluid to be drawn out. This causes a temporary vacuum and the water columns may become uneven as a result.
Next, the bacteria will begin to ferment the carbohydrates and create gas as a by-product. The gas will then cause pressurization with the jar and the water columns may again "reverse" into dissimilar heights.
Your kit is still working even if this does not occur. Sometimes there is not enough bioactivity to cause a noticable action; in other words, some vegetables (like cabbage) are very active fermentors where other vegetables (like asparagus) produce less visible activity.