Press salmon fillets between paper towels to dry surfaces thoroughly. Season on all sides with salt and pepper. Heat oil in a large stainless steel skillet over medium-high heat until shimmering. Add salmon fillets, skin side down. Immediately reduce heat to medium-low. Cook, pressing gently on back of fillets to ensure good contact between the skin and the pan, until skin is rendered and crisp, about 6 minutes. If skin shows resistance when you attempt to lift with a spatula, allow it to continue to cook until it lifts easily.
Flip salmon and cook on second side until a thermometer inserted into the thickest part registers 120°F for medium-rare or 130°F for medium, about 1 minute longer. Transfer salmon to a paper towel–lined plate to drain.
Divide rice evenly between 4 serving bowls. Top with diced avocado, cucumber, and scallions. Top each with a salmon fillet and spoon sauce on top, using the back of a spoon to evenly glaze each fillet. Sprinkle with furikake and/or sesame seeds. Serve immediately.