It’s true quite often, but not always. 月 (nichi)、日 (getsu)、夕 (seki)、木 (moku)…. Well these kanji probably have other on’yomi “more Chinese sounding” (I know 月 and 日 have much more on’yomi, and it may be the case for the other ones too…?).
So yeah, it is still true most of the time, but you can’t really use that to generalize. Still, if you happen to remember both the on’yomi and kun’yomi for a given kanji, but you forgot which is which, then indeed, many times the more Chinese sounding one will be the on’yomi ^^
I don’t really have ways to distinguish them other than learning the Textfugu way (learning on’yomi with stories, and kun’yomi with vocab).