In a large bowl, whisk together the pineapple juice, brown sugar, ketchup, soy sauce, chicken broth, ginger, and garlic. Reserve 1 cup of this mixture for later. Add the chicken breasts to the main bowl and coat thoroughly. Cover and chill in the refrigerator for about 30 minutes.
In another large bowl, combine diced pineapple, mango, avocado, chopped cilantro, and lime juice. Toss gently until well mixed. Cover and let sit while grilling the chicken.
Heat a grill pan over medium heat and lightly brush with oil. Drain the marinated chicken and discard the marinade. Grill each piece for about 6–8 minutes on each side until cooked through, occasionally basting with reserved marinade.
Remove the grilled chicken from heat and dice into small pieces. Divide the chicken among the mini corn tortillas and top with fresh salsa. Serve immediately.