I didn't use this method on my squares this time, but this youtube video shows an easy way to get mitered corners that would work well for this project if you want the self binding from the back fabric:
https://www.youtube.com/watch?v=Bfv1_vbrJB4&t=402s You just leave the lower fabric bigger on all sides by twice the width of your desired contrast edge. (This works for quilts of any size, too.)
I do have one quibble with the video: if you make the first fold on the border/binding
before you cut the corner off, the fabric on the underside will go all the way to the corner, and you won't have a risk of it curling back in the wash. However, the seam in the corner will be thicker, so maybe that's her reason for doing it as she does.