Rinse the rice until the water runs mostly clear, put it in the rice cooker pot, and add water up to the 2-cup line.
Add the soy sauce, cooking sake, and mirin. Lay the mushrooms and carrot over the rice, set the salmon fillets on top, and tuck in the dashi packet. Don't stir.
Close the lid and cook on the normal rice setting.
When done, remove the dashi packet and lift out the salmon. Peel off the skin, flake the flesh, remove any bones, and return the salmon to the pot.
Fold everything together gently with a rice paddle. Serve topped with sliced green onion.