Tuna should not be cooked “well”, it becomes really dry and loses it’s flavor. The idea is to sear it on the outside and have it rare on the inside, which is why you should buy “Sushi-grade” tuna for this recipe. Ask your local seafood market about sushi-grade fish.
Ceviches have their origin in Latin America and commonly consist of seafood (along with other ingredients) that is marinated in citrus. While the citrus “cooks” the fish almost like heat would do, it does not kill bacteria or parasites as well, so it is imperative that you are using freshest “sushi-grade” seafood for this.