Sprinkle salmon with 2 teaspoons olive oil, salt, and pepper. Stir the tomatoes, shallots, 2 tablespoons of oil, lemon juice, oregano, thyme, salt and pepper in a medium bowl to blend.
Place a salmon fillet, oiled side down, atop a sheet of foil. Wrap the ends of the foil to form a spiral shape. Spoon the tomato mixture over the salmon. Fold the sides of the foil over the fish and tomato mixture, covering completely; seal the packets closed.
Place the foil packet on a heavy large baking sheet. Repeat until all of the salmon have been individually wrapped in foil and placed on the baking sheet.
Bake until the salmon is just cooked through, about 25 minutes. Using a large metal spatula, transfer the foil packets to plates and serve.
