Originally Posted by
Rodin
Deus Ex Machinas in particular are from Greek plays where the stupid humans would get things so screwed up that nobody could fix it, and then the gods would come in and sort everything out with a wave of their hands while giving a moralistic lesson about how all of this could have been avoided.
Mistborn...isn't that. The first novel is inarguably a Deus Ex Machina by the modern definition - Vin gets superpowers out of nowhere that allow her to defeat the villain. However, the novel was clearly meant as part of a series and the "What the hell just happened" nature of the resolution is brought up by the characters as well - a clear indication that an explanation will be forthcoming.
The series as a whole definitely doesn't fit. In fact, it's kind of the opposite! What wasn't mentioned earlier is that the first person to get godlike power screws it up. Them screwing it up informs the backstory of the entire setting. And then the second person gets it...and makes things worse.
It's only after the plot is basically resolved (heroes dead, villains dead) that a secondary character takes the reins and his knowledge that had been established across three books is what allows him to stop the end of the world.
The one point where I can point to an unambiguous Deus Ex Machina is in the Wax and Wayne books, where literal God arranges for Wax to get his weapons back for the final confrontation of the first book. And even that is suitably lampshaded.