Hi Sophia,
This is expected behavior for Photoshop. When using Maps for Adobe in Photoshop the output file type is .tif, which doesn't support layers. As a result, you get a single rasterized layer for everything. In Illustrator, the output is a vector format which is why you see individual layers.
You could do a couple different things. If you want to use Photoshop, you can download each layer you want individually and you'll get a new layer in Photoshop for each download. Note that each layer will be a non-editable raster layer though.
You could also use Illustrator which supports raster layers as well as vector, so you'd get a layered output (including the raster layers) mixed in with the editable vector ones.
Hope this helps,
Steve