First, I must say -- I'm no expert! But this is the way I learned how to twirl a seam. It only takes two seconds to do it, and I'm happy with the way my center seams lay flat. Secondly, forgive the photography!!
Sew the two half square triangles with a quarter inch seam.
Press to the dark, or to the same side on both blocks. My iron wasn't hot yet, so the pressing isn't the best here.
Now you have opposing seams.
Nest seams and pin again. Then sew using a quarter inch seam.
This is what it looks like before you start twirling.
I darkened two seams on here with a pencil so you can tell, hopefully, the one that's important to remove. Not the slanted line on the left. You will be popping the thread on the vertical seam on the right.
Slide your seam ripper under the stitch that's closest to the long horizontal seam. For me there are usually three stitches in that quarter inch space. By cutting just the one closest to the long seam, the other two stitches pop out on their own. Flip it over and do the same thing on the other side. Note: I keep a seam ripper on my ironing board for just this thing. It really takes like two seconds to do this.
Turn the block over and open the seams. You'll see how it goes all by itself. The right side goes down, the left side goes up. The center of the seam is twirled.
Here I just press the center twirl with my finger to hold it open. (And I desperately need a manicure!) Then I place the iron on top of the whole block, or just the center if it's a large block.
Flip the block over and press with the iron on the right side. Ta-Dah!! A twirled center that lays flat.
I hope this helps. I am really lousy at explaining things. In case I confused folks, here's a blog that Judy did on the subject.