Why is making fruit punch on Shabbos not a problem of coloring?
אין צביעה באוכלין -- There is no [prohibition of] dyeing with respect to food.
Some relevant info from here:
Is one permitted to add food coloring to food on Shabbos?
One of the 39 prohibited labors on Shabbos is צובע or Coloring because in the process of the building of the Mishkan we find that they would dye wool that was used for making the coverings of the Mishkan. With regards to food however, the halacha is that אין צביעה באוכלין the actual translation of which states that coloring does not take place in edibles, which in turn means that one may blend foods and liquids even though one food item will color another. It is therefore permitted to add ginger to food, pour raspberry syrup into water, mix red and white wine and pour tea essence into hot water.
Am I permitted to add food coloring solely for the sake of coloring the food?
The halacha is that even adding coloring for the sake of coloring is permitted but the Mishna Berura writes that it is better not to do so. This does not mean that one may dye foods at whim. One is prohibited to dye food or liquids for marketing purposes. For example, one who sells liquor may not dye the liquor in order to make it more appealing to customers. Even though one is dying a food product and we could say that אין צביעה באוכלין, it is not so, because that is only true when the sole purpose is to whet an appetite. When the purpose is other than eating it takes on the regular laws of dyeing and coloring.