This is basically correct but a slight overstatement. It is true that this site is for questions specific to math.se (and those would, in general, not be on-topic for meta.se), yet I would not say that questions about site functionality are always better on meta.se.
Meta.se is for questions and discussions relevant to the entire network or at least to more than one site. A question is better asked there if input from or information of other communities (or SE) is relevant.
Questions that just also apply to other sites can go either here or there. Usually, standard support questions are better handled on a per site meta, and there is no point in directing those towards meta.se. Indeed, I would be against doing this.
More broadly, I do not think we should push users towards using meta.se. In the rare case that a question comes up here where it seems important it is on meta.se, we can point it out, but really it is rare.