John McCain Chicken Queso Burger

Name: John McCain Chicken Queso Burger
Ingredients: 1 lemon; 1 lime; 1 orange; 1/2 teaspoon chili powder; 1/2 teaspoon adobo all-purpose seasoning; 1 tablespoon extra-virgin olive oil; 6 6-ounce skinless, boneless chicken breasts; 3/4 cup fresh tomato salsa, plus more for serving; 6 slices pepper jack cheese (about 8 ounces); 6 challah rolls or other soft rolls, halved; 1 Hass avocado, sliced