This make-ahead punch is great to serve to a large crowd. If rum doesn't float your boat, you can replace it with vodka, instead.
Bring 3 cups water and first 3 ingredients to a boil in a medium saucepan, stirring until sugar dissolves. Remove pan from heat, and add tea bags. Steep 10 minutes; remove tea bags, and let cool.
Combine tea mixture, rum, and next 5 ingredients in a large container. Chill 1 hour or until ready to serve. Stir in Mandarin orange, lemon, and starfruit slices just before serving.