I think the main misunderstanding is that the n-layer is neutrally charged overall so it does not attract anything. 

Only in the depletion region is there an electric field. The electric fields acts to sweep electrons towards the n-layer and holes toward the p-layer. 

The depletion region partially overlaps both n and p doped layers. The part in the n-side is positively charged because the region is *depleted* of electrons which were once bound to the n-type dopants. This makes the n-side of the depletion region positive which attracts electrons towards the n-layer.