Whisk together soy sauce, lemon and lime juices, sugar, ginger, and sesame oil in a wide shallow nonreactive bowl.
Add scallops and marinate, covered, at room temperature, 5 minutes on each side (do not marinate any longer, or scallops will become mushy once cooked).
Transfer scallops to a plate and reserve marinade.
Heat 1/2 teaspoon vegetable oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then saute scallops, 6 to 8 at a time, until golden brown and just cooked through, 2 to 3 minutes on each of the 2 flat sides, transferring to a plate as cooked.
Wipe out skillet and add 1/2 teaspoon oil between batches.
Wipe out skillet again, then add marinade and boil until reduced to about 1/3 cup, about 2 minutes.