To prepare tuna, combine first 8 ingredients in a large zip-top plastic bag. Add fish to bag; seal. Marinate in refrigerator for 30 minutes, turning occasionally.
To prepare relish, combine watermelons and next 8 ingredients (through sesame oil). Cover and chill.
Remove fish from bag; discard marinade. Place fish on grill rack coated with cooking spray; cook 3 minutes on each side or until medium-rare or desired degree of doneness. Serve with relish. Sprinkle with sesame seeds, if desired.