To prepare rolls, rinse the rice thoroughly in a sieve. Drain well. Bring 1 1/4 cups water to a boil in a medium saucepan; add rice. Cover, reduce heat, and simmer 20 minutes or until liquid is absorbed. Remove from heat, and let stand 5 minutes. Stir in ginger, mirin, minced jalapeño pepper, shallots, sugar, fish sauce, and salt.
Combine soy sauce and 1 teaspoon sugar; brush over tuna. Marinate in refrigerator 10 minutes. Heat a nonstick skillet over medium-high heat. Add tuna to pan; cook 1 1/2 minutes on each side or until desired degree of doneness. Cut tuna into 8 (1/4-inch-thick) slices.
Add hot water to a large, shallow dish to a depth of 1 inch. Place 1 rice paper sheet in dish. Let stand 30 seconds or just until soft.
Place sheet on a flat surface. Arrange 1/4 cup watercress to cover half of sheet, leaving a 1/2-inch border. Top with 1/3 cup rice mixture; spread evenly. Arrange 1 tuna slice over rice. Fold sides of sheet over filling; starting with filled side, roll up jelly-roll fashion. Repeat procedure with remaining rice paper sheets, watercress, rice mixture, and tuna. Cut each roll in half diagonally.
To prepare sauce, combine vinegar and remaining ingredients. Arrange 2 roll halves on each of 8 plates; serve 2 1/4 teaspoons sauce with each serving.