You're right. When you pin the piece, it will curl up on the ends. You have to work with it curling up. And, when you sew both ends will continue to do this until you fold over to press. I found it easiest to put the circle fabric on top when sewing. I don't tear off the paper until the blocks are finsihed unless it comes off by itself. (Just be sure that the seams are facing in the right direction also.)
I know this sounds stupid maybe someone else can explain. Sewing these pieces is "nothing" like sewing anything else.
I wish my camera was working. I could take picks. I have pieces pinned ready to go. And I shoot them as I sew them. I'll see if I can find someone with a camera that works.