Your tileset has put tilesheets into the wrong slot.
A-Tiles are automatically the bottom layer, and you have to place tilesheets into exactly the same slot number they're supposed to go (A1-Tiles into A1, A2-Tiles into A2-Slot and so on.
The slots B to E are the top-layer-slot. That's where all the furniture and similiar things have to go into, then they will appear above the bottom tiles.
Note:
The first tile of the B-Sheet always needs to be transparent and set to star-passability, or the passability of the entire tileset will be broken.