Combine vinegar and mustard in small bowl; whisk in 4 tablespoons olive oil. Season dressing to taste with sea salt and pepper. DO AHEAD: Can be made 1 day ahead. Cover; chill.
Place 1 sheet of plastic wrap on damp work surface (to prevent plastic from slipping). Arrange 1/4 of tuna squares 1 inch apart in circle on plastic. Cover with second sheet of plastic. Using flat side of mallet, gently pound tuna squares until they are very thin and form an 8- to 9-inch solid round. Place tuna round, still in plastic, on plate. Form 3 more rounds with remaining tuna. Refrigerate tuna carpaccio at least 30 minutes and up to 4 hours.
Peel 1 plastic sheet from each tuna carpaccio round; invert onto plates and peel off remaining plastic. Brush each with 1 tablespoon olive oil, then sprinkle with lemon juice, chives, shallot, sea salt, and pepper. Toss watercress and 2 tablespoons dressing in medium bowl; season to taste with sea salt and pepper. Mound watercress atop and serve.
