the binding is attached to the quilt after the quilt is quilted and squared. quilting itself can change the size/shape of the quilt. just like applique.
you need to quilt it, then trim the backing/batting to match the top (at the same time ensuring everything is square) then attach the binding; usually machine stitched to the front then folded over to the back for hand stitching down. some people do press the binding to give it a more (crisp) edge. i think that is your choice. i have pressed when i felt it was needed, but other times did not bother.