I keep sweet soy like kecap manis and 醬油膏 in the fridge because occasionally it can catch mold otherwise. I do the same with sweet vinegar like balsamic. However I think this depends a lot on how hot and humid your environment is. In cool and dry climates it's probably not necessary.

醬油膏 = soy sauce paste

It’s one of my favorites. I try to find ones without much additives and refrigerate after opening to keep it fresh.

Every soy sauce label I remember seeing has said, "Refrigerate after opening." I don't know why this seems to be rarely done (at least in the US).

Yeah I just follow food safety instructions on packaging

I have feeling that I should do it. The difference between open bottle that have stayed outside and fresh bottle is pretty clear. Refrigeration would slow down any reactions and thus keep taste better longer.