To make the teriyaki aioli, combine garlic and salt in a small bowl until a paste forms. Add in the teriyaki sauce to the mayonnaise. Then, whisk in mayonnaise, olive oil, and lemon juice. Season to taste with kosher salt and pepper. (NOTE: You can make this aioli one day ahead. Keep refrigerated until ready to use.)
Preheat barbecue. Brush pineapple slices with olive oil on both sides to prevent them from sticking to the grill. Place pineapple and hot dogs on the barbecue and grill until pineapple is nicely glazed and the hot dogs are cooked through and browned on the outside, about 7-9 minutes. If the pineapple is done first, remove the slices from the grill and set aside.
Place one cheese slice on each hot dog. Close the barbecue for 1-2 minutes to let the cheese melt.
Lightly brush the inside of your hot dog buns with olive oil and place on grill for 1-2 minutes.
Remove hot dog buns from grill and place on a serving platter. Insert one hot dog into each bun and top with grilled pineapple, chopped mango, jalapeño peppers, diced tomatoes and sliced red onions. Drizzle with teriyaki aioli and serve immediately with extra sauce on the side for dipping.