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.