In a large pot, bring 6 qt. water and 2 Tbs. salt to a boil. Add the fusilli and cook until al dente, 12 to 15 minutes. Drain the pasta and toss it immediately with 1 Tbs. of the olive oil. Let the pasta cool completely in the refrigerator.
Heat a charcoal or gas grill to medium-hot. In a blender or food processor, purée the cumin, paprika, turmeric, cayenne, garlic, onion, the chopped cilantro, the parsley, lemon juice, 8 Tbs. of the olive oil, and salt and pepper to taste. Put the mixture in a large bowl.
Brush the tuna with the remaining 1 Tbs. olive oil, season it with salt and pepper, and grill it over a medium-hot fire for 6 to 8 minutes, turning occasionally until it’s cooked to the doneness you like. Remove from the grill. When the tuna is cool enough to handle, slice it into strips or break it into 1-inch pieces.
Add the fusilli to the sauce and toss to combine thoroughly. Season to taste with salt and pepper. Put the salad in a serving bowl and garnish with the tuna, the whole cilantro leaves, and the lemon wedges.
The fusili can be tossed with the sauce and held in the refrigerator for several hours. Let it come to room temperature before garnishing with the tuna, cilantro, and lemon wedges.