Their stones are also curved.
Indeed, but mine aren't. I use a diamond plate (DMT or Atoma depending on my mood) to flatten my stones before use. The trick to getting a smooth, even convex is a combination of three techniques:
a) using the right amount of pressure--
Waterstones are not completely rigid. They flex somewhat under pressure. (You can see this when you lay a freshly-used waterstone on a granite reference block, shine a light in between the two to reveal a gap, then press down hard on top of the waterstone. If the gap of light is small enough, it will disappear.) In addition to that, once you work up a bit of slurry, the water-suspended abrasive particles are compressed into the stone as the knife is stroked over them, then rise up out of the surface again as the blade goes past. In this manner, the suspended particles can hug the surface of the blade along a tiny, tiny convex arc.
b) controlling the wear pattern of the stone--
You sometimes want the stone to dish a little bit but not too much. Once you have, in your judgment, the right amount of concavity in the stone, you can prevent any further sigificant amount of dishing by trying to evenly utilize the entire surface of the stone.
c) a rolling wrist action--
Hard to describe, but it is what it sounds like.