My interpretation of the IELTS criterion of "idiomatic usage" is that the way the language is used is "natural" in the sense of native speaker usage, NOT to be confused with knowing/using a lot of idioms.
In other words, the language doesn't sound as if it comes out of a language textbook, but as if the person has had exposure to and experience with the language as it is actually used in an appropriate environment.
So, trying to construct an example:
(a) This cultural knowledge was transmitted from one generation to the next.
(b) One generation learned the cultural knowledge, then explained it to another generation.
Although both sentences are correct, and neither uses an "idiom," I would consider (a) a better instance of idiomatic usage than (b).
Other people may have a different interpretation of what the criterion means. If so, please share it!