Does vinegar need to be refrigerated after being opened?
If in doubt, follow the instructions on the label - since this is a vinegar with extra flavoring, all speculation on whether it could spoil (by oxidation of flavor compounds) or even become unsafe to consume is just that: speculation.

Also, make sure that vinegar is stored with the lid down tight if not refrigerated: Asian bottles are often badly designed (caps that tend to stay half open or not seal well), and a half-open vinegar bottles can attract fruit flies and similar surprises into it.