I do very little handwork at all so can only offer some general advice. Is the kit a small project or a bed sized project? If it is a small project it may be designed to be pieced/quilted/sewn all at the same. Usually you do the applique on your fabric before you have batting anywhere near it. Are your turtles stuffed? In that case I could see where you would stitch through batting.
We also have a lot of similar terms that can mean different things to different people. So are you sure it is batting and not fusible interface of some sort??