Think in 3D: rocker works together with the reverse sidecut. Wakeboards and surfboards have rocker. The idea, I believe, is that since you're riding on a fluid, the board causes the fluid to take the shape of the turn. This is the opposite of riding on a solid (packed snow) - the solid causes the board to take the shape of the turn. So it would make sense to me that the boards would have to be shaped oppositely.
I think this is what's going on: since the widest part of the board is in the middle, when you tilt the board up on edge, the middle of the board goes deeper into the fluid than the ends. This provides your base of support. Since the ends of the board are far less deeply submerged, they are free to be pushed around. So the middle of the board becomes the pivot point for turning.
Hmm... maybe standing with your front on or just behind this pivot point is the way to go... hence the overall shape of the swallowtail boards. I don't know why that tail shape came about though... seems like a surfboard style pin-tail would be effectively equivalent, more durable and easier to build.
I dunno, I just came up with that just now. I think riding powder or water is more dependent (completely dependent?) on steering - I don't think any board shape will turn itself just by being tilted up on edge like a board will on solid snow. EDIT: No... wait, I think a board with rocker and reverse sidecut would turn itself in powder, when tilted up on edge. The rocker would make the board want to turn, the reverse sidecut would help the board pivot.
Anyone?