The drift causes the spin, if you have it set up properly.
And if it's moving along fast enough, obviously.
I also still don't understand why the presence of a float makes this way of using a spinner more successful.
I believe it's just another method, not necessarily more successful. One advantage would be that you can cover more water, as the blade is able to drift through a run rather than being retrieved across it. You can just certainly cast and retrieve, especially in slower moving water/across pools, with similar success. However, you can also cast and retrieve with a float, so this rig is multipurpose. The float can also help to keep your gear off the bottom, so if you know where that is you can set your depth so that you can let the gear sink and not be too worried about losing it. The alternative is to use the "countdown method" without a float...
Slow and low is recommended because that's generally where the salmon are holding and they aren't necessarily going to chase your lure if it's 10ft. above them or moving too fast.
Keep in mind that these are all just recommendations, based on experience, and not "gospel." Feel free to experiment with techniques and find what works best with you and the conditions you fish.