In a large bowl, combine ingredients for marinade: sesame oil, rice vinegar, lime juice + zest, agave, tamari, cashew butter, and ginger. Mix well. Pour marinade into a large resealable plastic bag. Add watermelon chunks; seal bag, and chill for 2 hours.
Heat a large nonstick skillet over medium. Remove watermelon from marinade; set marinade aside. Cook watermelon, stirring often, 4 to 5 minutes. Add reserved marinade; cook 2 to 3 minutes, until slightly thickened. Transfer watermelon mixture to a bowl and chill for at least 30 minutes.
Prepare rice according to package instructions. Divide cooked rice evenly into each of 4 bowls. Top evenly with watermelon, avocado, green onion, and other optional toppings, if desired. Top each bowl with 1 to 2 tablespoons of sauce.