I don't see any obvious issues with your map file. Seems my earlier thinking was wrong - there definitely aren't any old properties hiding in here. Your layer orders look good too.
Looking again at the screenshot, I'm thinking now that it's actually the way you've chopped those sprites up that's the problem, in which case it's likely I've just explained how this part works poorly!
In Tiled, layers are per-map so anything rendered within the second layer will overlay anything rendered in the first layer, i.e. Tiled is drawing everything in your ground layer from the top of the screen down, and then drawing everything in your buildings layer from the top of the screen down. So in Tiled, something rendered on the building layer in the middle of the screen will overlap something rendered on the ground layer just one tile below it. Is this making sense?
In Qiso though, layers are per-tile, not per-map. Like Tiled, Qiso starts at the top of the screen and works its way down, but it iterates every layer of the tile at the top, draws each sprite, then moves on to the next tile. The primary reason for this is so that you can have things like a tall building on one tile that overlaps the tiles further up the screen from it, but also have something like a grass with 'sticky up bits' overlapping the base of that building on the tiles directly after it. Notice how the sample grass tiles provided cover the bottom of the sample walls provided?
So, this in mind, it looks like your current sprite slices are horizontal. Slice them vertically instead and you should see better results.I.e. each sprite wants to be the width of the tile it's on, but give them a canvas of say... 4x that size, so that the full height of the completed building shows. If you want to send me the original unsliced version of that white building I'll slice it up for you to show what I mean - I feel like my explanation is making this sound more complicated than it actually is! Feel free to private message the file if you'd rather not post it publicly here.