A couple of things. If you are just beginning needle turn appliqué purchase as tightly woven fabric as you can. Batiks are great. Next. Inside points clip like you are. Turn the edge under as far as you have clipped then bring the thread up from the bottom a few threads beyond the clip. For your next stitch do an overcast going front to Back only through the appliqué piece, coming up again beyond the clip. Now pull this stitch down TIGHT. Notice that the raw edge has now started to turn. If you still have a bit of fray you can do more than one overcast. As far as outside points ALWAYS ALWAYS take two stitches at the point to lock that point in place. Turn the point and continue on.
hope this helps