To grill the tuna, get a charcoal or stove-top cast-iron grill very hot. Brush the fish with olive oil, and sprinkle with salt and pepper. Grill each side for only 2 to 2 1/2 minutes. The center should be raw, like sushi, or the tuna will be tough and dry. Allow to rest for 5 to 10 minutes and serve.
Combine all ingredients in a large bowl, except tuna steaks, mix thoroughly and season with salt to taste. Set aside or chill in the refrigerator.