Mix soy sauce, ponzu sauce, sesame oil, oyster sauce, black bean sauce, chili paste, ginger, and garlic.
Rinse fish, pat dry, and coat with half the ponzu mixture. Let stand about 10 minutes. Discard liquid.
Set salmon, skin up, on an oiled grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook salmon, turning once, until opaque but still moist-looking in center of thickest part (cut to test), 6 to 8 minutes. Remove from grill.
Mix salad greens with remaining ponzu mixture. Present fish on or beside salad.