Your confusion about the magnet placement is a matter of context.
Assuming one magnet disk you want the north pole of a magnet over one coil leg while the next magnet (which will be a south pole) is over the opposite leg. This will give you the effect of "as a north pole leaves the COIL, a south pole is entering".
Now the second disk with its magnets aligned over the first disk but with the opposite magnet poles dramatically increases the flux passing through the wires of the coil legs. Think of the second disk as "sucking" the flux lines of the first disk so they stand straight out from the magnets. This way the coils make a nice perpendicular slice through the flux lines which gives you the maximum generated power.