The explanation:
Dish detergent has a material called a surfactant, or surface active agent. The molecule has two ends, a head and a tail. One end likes water and lowers the surface tension. The other end likes fats and lipids and dissolves fats which is why they can clean dirty dishes. In this demonstration, the surfactant is dissolving the fat and the water portion is attracting the food color. I will post other demonstration on chromatography and chemical clocks at another time. If you come up with an interesting idea, please pass it along in the comments. By the way, Don't drink the milk...