Mine do this if I stretch the edges of the quilt and pull those seams just ever so slightly apart. Let the edge of the quilt relax, then lay the border (nice and flat) on top.
If the outside edge of your pieced center is a little ruffly, it's magnified in the borders. So lay the quilt down, lay the border on top, put a little stretch in the border when pinning, and feed through the sewing machine with the border on top. The feed dogs will help.
Good luck.