1. Combine rice and 1 1/4 cups water in a medium saucepan over medium-high heat. Bring to a boil; reduce heat to low, cover, and cook 20 minutes or until liquid is absorbed (do not uncover while cooking).
2. Remove pan from heat; let stand covered 10 minutes.
3. While rice stands, combine 2 tablespoons vinegar and sugar in a small microwave-safe bowl; microwave on HIGH 30 to 45 seconds or until boiling. Stir mixture with a whisk until sugar dissolves.
4. Add cream cheese and 1/2 tsp. salt to bowl, stirring with a whisk to combine. Gently fold vinegar mixture into rice using a rubber spatula; let stand 5 minutes.
5. Generously coat 12 muffin cups with cooking spray. Lightly coat each of 12 (5-inch square) parchment paper pieces with cooking spray; press paper squares into muffin cups to form a liner. Using moistened hands, press rice mixture evenly along bottom and sides of muffin cups (about 21/2 tablespoons rice per cup). Refrigerate 30 to 40 minutes.
6. Combine remaining 2 teaspoons vinegar, remaining 1/2 teaspoon salt, soy sauce, oil, and red pepper in a medium bowl, stirring with a whisk.
7. Add cucumber, tuna, onions, and avocado to bowl. Toss gently to combine.
8. Divide tuna mixture evenly among rice cups; sprinkle evenly with sesame seeds. Gently remove cups from pan by lifting parchment paper edges.