Mentos have a strange chalky color and texture and they do taste rather like antacid tablets. If the chalkiness comes from carbonates, the fizzing might be explained as a neutralization reaction that produces CO2.
But the ingredients don't include carbonates- or any other significantly alkaline material. All variations of Mentos contain sugar, glucose syrup, hydrogenated coconut oil, gelatin, dextrin, "natural flavor", corn starch, and gum arabic. They're basically just a big pellet of flavored sugar with gummy stuff added to give them structural integrity and to keep them from sticking together in the package.
So why do Mentos make diet soda foam so violently? It's a physical reaction, not a chemical one.
Ordinarily, water resists the expansion of bubbles in the soda. Water molecules attract each other strongly, and they link together to form a tight mesh around each bubble. It takes energy to push water molecules away from each other to form a new bubble, or to expand a bubble that has already been formed. The phenomenon is called "surface tension".
Now drop a Mentos into the soda. The gelatin and gum arabic from the dissolving candy disrupts the water mesh, so it takes less work to expand bubbles. At the same time, the roughness of the candy surface provides many little nooks and crannies that allow new bubbles to form more quickly (a process called nucleation). As more of the surface dissolves, both processes accelerate, and foam rapidly begins to form.
You can see a similar effect when cooking potatoes or pasta in a pot of boiling water. The water will sometimes boil over because organic materials that leach out of the cooking potatoes or pasta disrupt the tight mesh of water molecules at the surface of the water, making it easier for bubbles and foam to form. (See also: Why does adding oil to cooking water keep it from boiling over?) Root beer can also foam over if a scoop of ice cream is added, for essentially the same reason. The surface tension of the root beer is lowered by gums and proteins from the melting ice cream, and the CO2 outgassing from the root beer blows the foam.
