I have also found that when sewing down the second side, my corners miter much neater and sharper if I make the fold from the bottom edge into the corner before making the turn. I'm not saying that well. Let me try to be clearer.
After sewing the binding onto the first side of the quilt (the back for me), I turn it over and sew it by machine to the front. I also use the no iron method with my binding.
As I am approaching the corner, I fold the BOTTOM edge up and into the corner and lap the SIDE I am sewing over that. This allows me more ability to adjust the miter before sewing it down, and when I sew the side into that corner, I can stop and turn with exactly the same distance from the edge as I had on the side.
I used to fold the bottom over the side and my miters were much less satisfactory to me.