Make the teriyaki sauce by whisking cornstarch with water in a medium bowl. Add remaining sauce ingredients and bring mixture to a boil. Reduce heat and simmer for 7 to 10 minutes. Let cool before you use it for marinating .
Set aside 1 cup of the sauce. Use remaining sauce and pour over the chicken tenderloins in a medium bowl. Cover and let marinate 6 hours.
Preheat a large skillet over medium low heat. lightly oil skillet and saute chicken in a pan for 8-10 minutes or till cooks through and browned. slice each chicken into 3 or 4 pieces and put in a medium bowl.Microwave the reserved cup of teriyaki sauce for 30-60 seconds and pour sauce over sliced chicken in the bowl.
Preheat another skillet over medium heat. Toss a tortilla into the pan for a minute, then flip over and add 2 to 3 tablespoons of shredded cheese across the center. Let tortilla sit in pan until cheese starts melting. Remove tortilla and spoon equivalent of 1 chicken tenderloin into the tortilla. Spoon about 1 teaspoon of teriyaki sauce ( from reserved sauce poured over chicken) over the chicken in each taco.
Arrange the rest of the taco with shredded lettuce, 1 or 2 tablespoons of pineapple and tomato, and a few green onion pieces. Repeat the process for the remaining tacos.