When I machine sew binding I also do the faux flange Tartan suggested. I do press it in half. The flange technique calls for stitching to the back first then folding over to the front. I then glue baste in place with washable school glue and set it with a hot iron. I use a walking foot for all steps. I don't have any issues.
Here is a good tutorial from the QB by Charismah.
Quick Machine Binding with Flange