normally a fusable product is used when doing raw-edge applique- that is why it is not turned under- and the fusable protects those edges- after fusing to the background a satin stitch or blind hem stitch or zigzag is usually used to go around the block. the fusable keeps the edges from fraying and pulling away with wear and laundering
if you do not want to use a fusable another way to do it would be to use either lightweight muslin or tule...place right sides together= stitch around the applique piece- cut a slit into the muslin (or tule) and turn the block so the muslin is on the back and you have a finished edge on your applique pieces. then you can stitch them down any way you want to with no raw edges.