The background fabric isn't sufficiently stable. What I do for applique is heavily starch the background fabric before cutting, using a 1:1 solution of STa-Flo liquid laundry starch and water. I toss the yardage in the dryer, then iron with steam. The fabric comes out stiff enough so it doesn't distort, even with satin stitch (which tends to tunnel).
As someone else mentioned, it's also a good idea to cut your background pieces over-sized so that after the applique is done you can trim to correct size.