Perhaps I'm not understanding your question. When doing applique, I use a very tight zigzag stitch with a satin stitch foot or open-toe embroidery foot (so the thickness of the stitches do not create buildup under the presser foot). Set the tension so the bobbin thread stays mostly under the fabric so the top thread is the only thread that shows on the top (sometimes threading the bobbin pigtail will help).
Fuse the cutout fabric to the backing fabric. Then zigzag so the raw edge of the fabric is covered by the zigzag (helps to use a thicker thread so the coverage is easier).
Some newer machines have the ability to miter corners. On my 930, I set the needle position to the outside of the raw edged. Then when I near the corner, I gently, but consistently, narrow the stitch width to an an outside point, since the needle on the outside edge, turn the fabric and gently, but consistently, widen the stitch to full width. This creates a nice mitered corner.
When making curves, stitch small lengths and then sink the needle on the outside of the curve, and gently turn the fabric to follow the curve and repeat while going around the curve.
https://books.google.com/books?id=MQneD8cQ5KAC&pg=PA13&lpg=PA13&dq=mitered+applique+corner&source=bl&ots=1sHsUrkVAz&sig=1WZ-i2-T3RtvUEW797sHxTKiq4E&hl=en&sa=X&ved=0ahUKEwiaoZeiwunKAhVslYMKHewdDFEQ6AEIKzAC#v=onepage&q=mitered%20applique%20corner&f=false How to Appliqu Like Pro Sew4Home
(FWIW, IMHO, the satin stitch on the bird is really a poor example. The stitch is not very even at all--could be the sewing machine.) How to Make and Apply Appliques
(The giraffe is a better example, although choosing a simple design to applique usually yields better results.)
Practice, practice, practice!