Pat dry the salmon cubes with a paper towel and set them aside.
In a medium bowl, combine the ingredients to prepare the teriyaki sauce: soy sauce, lemon juice, brown sugar, garlic, ginger, salt, and pepper.
Place the salmon cubes in the bowl and pour approximately 3-4 tablespoons of the prepared teriyaki sauce mixture over them. Allow the salmon to marinate for at least 30 minutes.
While the salmon is marinating, heat a skillet with oil over medium heat. Take the remaining sauce mixture and add a teaspoon of sesame seeds to a saucepan. Heat the mixture over medium heat, bringing it to a boil, and allow it to slightly thicken.
Add the marinated salmon cubes in a single layer, and cook for 4-5 minutes. Flip them and continue cooking until the salmon is completely cooked through.
Once done, garnish the salmon cubes with sesame seeds and chives. Serve the salmon cubes over the rice and enjoy.