The truth is…you can’t be 100% sure! Producers of pigments and inks are not obligated to divulge the ingredients of their products. Pigments and tattoo inks are not regulated by the US Food and Drug Administration. An artist who mixes their own inks from dry pigments would be most likely to know the exact formulation of the inks. Keep in mind the information is usually proprietary (a trade secret), so you may or may not get answers to your questions.
Most tattoo inks technically are not inks at all. They are a composition of pigments that are suspended in a carrier solution. Contrary to popular belief, pigments are generally not vegetable dyes. Modern pigments primarily consist of metal salts. In addition, some pigments contain plastics and there are some vegetable dyes as well. The pigment provides the color and the carrier disinfects the pigment suspension, keeps it evenly mixed, and accommodates ease of application.