Thanks ninnie and bill's wife!
If anyone else does that tutorial, I think they forgot to mention that you stop short of the center by a quarter inch with your seams, so the seams can swirl in the center and it will lie flat. Sew from the outside into the center, and press the seams going up on one side and down on the other so they nestle to match up the seams while sewing the last center seam.
It is something about coming from a russian blog. They didn't explain all that part, you just had to know it.