In the past before I realized that all the bindings needed to have more than a single seam holding them on, I have used the pre-made satin binding and finished a blanket off with it by just inserting the edges of the blanket into the binding and sewing it on. I always used a straight stitch.
I thought I would let the experts give us their opinion. I went to the Youtube website and searched for Sewing a satin binding on a quilt. These were a couple of the videos.
https://www.youtube.com/watch?v=I5T2N6cEQvM
https://www.youtube.com/watch?v=w6u3tbcXBgY