Rinse the rice in a strainer until the water runs clear. Bring 2 cups water, the rice and 1/2 teaspoon salt to a boil in a medium saucepan. Reduce the heat to low, cover and cook until the rice is tender and the water is absorbed, about 20 minutes. Let sit, covered, 10 minutes.
Meanwhile, combine the vinegar, sugar and 1 teaspoon salt in a small microwave-safe bowl and microwave until the sugar is dissolved, 30 seconds to 1 minute; stir. Transfer the rice to a large bowl. Add the vinegar mixture and stir with a rubber spatula until the rice is fluffy but still sticky, 2 to 3 minutes; let cool completely.
Bring a small saucepan of salted water to a boil. Add the edamame and cook until tender and bright green, 3 to 5 minutes. Drain and rinse under cold water until cool.
Combine the scallions, lime juice, orange juice, soy sauce, sesame oil, ginger and 1/2 teaspoon salt in a large bowl. Add the tuna and edamame and stir to coat; season with salt. Divide the rice among bowls and top with the tuna mixture and cucumber. Sprinkle with sesame seeds.