That video was made a year or two ago and is of poor quality (video and yarn color(s) for the video). Be that as it may, I will make an updated version soon (once the cool winds that signify the slumber of summer come a-calling).
Anyway, the idea is fairly simple–the extra yarn(s) ride on top of the row that’s being built upon. You do your loop over and around them letting the crocheted knot cover them. The color that you’re pulling with the hook is the color that shows.