Yes, those are the edges I'm talking about. And they do matter, because you want the parallax shader to treat the faces as flat surfaces, but they won't get treated that way unless they are separated from the other surfaces. See the smooth shading in your screenshots? That's because they're connected. You don't want that in this circumstance.

If they're being projected in the reverse (it's hard to tell from your screenshots), try inverting the height map. I've never used the built-in parallax shader, so I can't really give you much information about how it works.

Jibb