In a large bowl, combine the salmon pieces with 1 tablespoon light soy sauce, 1 tablespoon sriracha, and 1 teaspoon sesame oil; mix to coat and refrigerate to marinate for at least 30 minutes.
While the salmon marinates, cook sushi rice according to package instructions and steam the edamame; keep warm.
Whisk together 2 tablespoons mayonnaise and 2 tablespoons sriracha in a small bowl to make the spicy mayo; set aside.
Heat 2 tablespoons vegetable oil in a large skillet over medium heat until shimmering.
Add the marinated salmon to the skillet in a single layer and cook 5–6 minutes, turning as needed, until cooked through; cook in batches if necessary to avoid overcrowding.
Remove the cooked salmon to a bowl and keep warm.
Divide the cooked sushi rice among four bowls as the base.
Top each bowl with spicy salmon, steamed edamame, sliced avocado, and sliced cucumber.
Drizzle spicy mayo over each bowl, then sprinkle furikake and chopped green onions before serving.