The only requirement is for the front wheel to TOUCH the line so it doesn't matter if the line is crossed or the whole bike goes over it. Doing anything other than just nicking the line wil be costly in time, but missing it entireley might be even more costly which is why the degree of skill required to make the best of this obstacle is quite high.
I do have a few questions regarding the explenation about the Jink.
There are a large number of Adachi Special obstacles, but the more esoteric of them only tend to be used only when the riders involved have a great deal of practice under their belts. The Jink (in singles or multiples) is the most commonly used because it is quite easy for even a novice to understand.
Dedicated to the wonderful sport of Moto Gymkhana