I live in the tropics and never refrigerate oyster sauce or soy sauce. I don't use 'black bean sauce' but have a jar of black beans also never in the fridge.
Preserved vegetables don't need refrigeration. That was the point of preserving them in the first place.
I'd say mayo would need refrigeration, but I make my own and use it very quickly, so it's never in there more than a day or two..