Mix the curry paste and lime juice together in a small baking dish. Add the salmon to the curry mixture and turn to coat evenly. Cover the dish with plastic wrap and place in refrigerator for 1 hour.
While the salmon is marinating, make the chutney by stirring together the nectarine, plums, blueberries, onion, cayenne pepper, cilantro, lime juice, salt and pepper in a bowl. Place chutney in refrigerator until salmon is ready.
Preheat oven to 425 degrees F (220 degrees C).
Remove plastic wrap from salmon and bake in the preheated oven until salmon flakes easily with a fork, 12 to 15 minutes. Spoon chutney in even amounts over each fillet.