It's mentioned somewhere in the manual, but you want to make sure to use Floor tiles only on the bottom floor of your maps, and don't use Modifiers on floor tiles. If you want to have multiple floors, you need to use Wall tiles and the player can run on top of the Wall tiles as if it were a floor! And for the stairs themselves, they should be made out of Wall tiles with modifiers.
That sounds confusing I know, but basically the Floor tiles are only supposed to be used on the bottom layer of a map. When you use Floor tiles on any layer above that, they will not display properly