Slice melons thinly and lay on a large shallow platter. Slice tomatoes crosswise and lay on platter with melons.
Whisk together lemon and lime juices, chiles, brown sugar, 1 tsp. salt, 3 tbsp. oil, the ginger, and 3/4 tsp. peppercorns. Pour all but 2 tbsp. dressing over melon and tomatoes. Let marinate 10 minutes.
Meanwhile, heat a large (not nonstick) frying pan over high heat. Pat scallops dry and season with remaining salt and pink peppercorns. When pan is hot, pour in remaining 2 tbsp. olive oil; place scallops one at a time in pan, spacing evenly; and cook until golden brown and crusty, 2 minutes. Turn over and cook on other side, 1 minute.
Add warm scallops to platter, drizzle with remaining dressing, and serve.