There is more than one type of pre-made corn tortillas that you can buy in the store. What you'll find in American grocery stores are shelf-stable, and those don't really benefit from refrigeration, as you've mentioned.
In Latin markets, you will find that type, but you will also find them in the refrigerated section. Those must be kept cold. If you don't, they will mold. And even in the fridge, they'll develop mold after a week or two. (and it's a pain to go looking between every tortilla for signs of white mold (purple and green are easy to find).
What's most important for these two isn't so much about how they're stored, but how they're reheated. For tacos, you want to heat them up in pairs on the griddle. This keeps them thick enough that the top won't flake up badly on you. The space between the two tortillas will steam, and you'll be able to get a bit of a crust on the two outer sides if you wish (but that will make it less flexible, potentially leading to tortilla failure.) Keep the two together as you assemble your taco, and you won't have any problems.
The third type of tortilla that I'm familiar with are the Salvadoran style. These are about a 1/4" (6mm) thick, and made from a much finer grind of corn. They just don't work for tortillas, as when heated, they only fold a little bit. These are better for the sort of things you'd use tostadas for. (they're not arepas ... they're thinner than those and the flour is different, and they're not stuffed like a pupusa, either)
For these, you'll want to heat them slowly, so they don't end up too rigid, but you can cook them separately as they won't have issues with flaking up like thinner tortillas from coarser cornmeal will.