Your question is neither sufficiently specific nor detailed to provide a proper answer. However you provide a clue as to how it is possible to disperse the more water-loving components in a fatty matrix without the use of emulsifiers listed explicitly as such in the ingredients list. Assuming that 1) the product is bona fide - the composition is as listed; and 2) the pigments are only of limited fat-solubility; then evidently one or more of the constituents has to provide the required emulsifying activity.
My guess is it is butter, which is an emulsion of water in fat. I would guess the water-loving ingredients are dispersed in the butter before blending in the remaining fatty components, but that is an educated guess.
As for the absence of preservatives, I would guess the low water content would limit bacterial growth. There are available certainly guidelines regarding such matters.There are available certainly guidelines regarding such matters.