Hi,
Should I treat what is in a pair of quotation marks just like an adjective without any difference in terms of whether to place an article or not? Yes.
I feel like you have to have an article, 'a' or 'the' or 'an', before a quoted content acting as an adjective for a singular noun. With a singular countable noun, yes, you need some kind of determiner.
... reveals an aspect of 'pali-pali' Korean culture. This is fine.
-- The 'culture' is an uncountable, I think. Yes.
Best wishes, Clive