Well, this does not surprise me. If you move the spoon in circles, you create a shearing action between the faster moving spoon and the slower liquid. This is where you create a force that makes the two different liquids mix. If you move it back and forth, you still have the shearing action between the spoon and the liquid and it is the same as before, as it only depends on the size of the spoon and speed and length of movement, but also the action of the liquids knocking into each other. This is a stronger force than by going in circles as the molecules crash into each other, instead of side-by-side.
Of course, the difference in technique depends a lot on how much force the liquids need to mix in the first place. So, you should be able to easily verify this if you use water and oil and try to mix them by stirring in circles and going back and forth. The difference should be noticeable, while the difference for water and ink should not be detectable.
I don't know the Japanese research, but Harold McGees 'On Food and Cooking' confirms this in the section about whipped cream, how this force allows the fat globules to destabilize (and finally end up as whipped cream).