I haven't watched the videos, but here's how this could work --
If you shake oil and vinegar together very vigorously to make a quick salad dressing, you know how it will stay mixed at least for a short time? This is an example of a short-lived mechanical emulsion. The emulsion is unstable -- it might last for only a minute or so, and then the fat and vinegar will separate. But while it's sufficiently mixed, it would have a consistent composition.
If you mix the lye and fat together briefly but vigorously, you can create a similar temporary emulsion that could last long enough so you could separate out the batter for coloring. In the short time that the mixture is emulsified, the soap batter is going to be fairly consistent, but you'd want to divide the batter quickly or risk getting some lye heavy portions and other fat heavy portions. The divided portions of batter then have to be mixed sufficiently to form a truly stable emulsion before the soap is poured into the mold.
It's an advanced technique that I wouldn't recommend to a beginner, but I can see why people might do it in the interest of getting the maximum working time out of their soap batter.