User blog comment:JadenLan/New information about Remnant from WoR Vytal Tournament Festival/@comment-410526-20151010161931

Actually I think Atlas probably has a large Dust reserve of its own. In "The Shining Beacon," Weiss mentions that the Dust she brought to Beacon is mined "directly from the Schnee quarry", and Sun also mentions a big shipment of Dust coming by sea "from Atlas" in "Black and White." Given that the SDC is based in Atlas, I'd say it's safe to assume that they mine their own Dust there and ship it to the other kingdoms. I'd actually go as far as saying that Atlas is the most technically advanced kingdom because of their large Dust reserves.

So I think that the dynamic between Atlas and Mistral is reversed; Mistral needs Atlas for Dust rather than the other way around. That said, I'm fairly certain that all of the continents have their own reserves, though they are probably much more limited or lack the infrastructure to extract and refine it, which is why it is cheaper and simpler to just buy from the SDC and Atlas (now that they're at peace).

Other than that I think what you said makes sense. Maybe Atlas likes to use their Dust in technology (firearms, robots, etc.) whilst Mistral uses it in a more traditional way, like weaving it into clothing or combining it with their bodies sort of thing. At least during the Great War era, if the diagram above is anything to go by. Also note that Cinder claims to be from Mistral, if that was true.