Heat grill to medium-high. Once it is hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate.
Toss the watermelon, cucumber, mint, lime juice, 1 tablespoon of the oil, ½ teaspoon salt, and ¼ teaspoon pepper in a medium bowl.
Mix together the ketchup and 1 tablespoon of the Sriracha in a small bow.l
Rub the onion with the remaining teaspoon of oil.
Gently mix together the pork, soy sauce, garlic, and the remaining 1 to 2 tablespoons of Sriracha with your hands in a large bowl until just combined. Form the mixture into four ½-inch-thick patties.
Grill the onion until 4 to 6 minutes per side for medium. Grill the burgers until cooked through and an instant-read thermometer inserted in the center registers 145° F, 4 to 6 minutes per side.
Stack the ketchup mixture, lettuce, burgers, and onions between the buns. Serve with the watermelon salad.