I just did my first circle into square last weekend (yeah, I know I'm late but all the circles are done and actually almost done with the 9 applique blocks too). I put it off because I knew that doing this was going to be a BEAR! Well, I had an epiphany! I used Sharon Schamber's Piecelique technique and it was so easy!
If you do a YouTube search on Sharon Schamber Piece Lique you will find the technique. Just imagine that I used a circle of doubled freezer paper with the center circle cut out to turn under the seam allowance around the inside of the circle in the square of fabric, clipping the curve first. Layed it on top of the star, glued it down, then sewed it to the circle. It came out PERFECTLY with no problem, no fusing, no lining up edges.