Are you just sewing a strip of fabric on for the borders and cutting off anything left over? Fabric creeps, particularly the bottom fabric because of the feed dogs. Cut borders to fit, and hold on to your fabric layers as you sew so it doesn't creep. It can also make a difference if you cut your borders lengthwise rather than cross grain, cross grain (selvedge to selvedge) has more give which isn't always your friend.
I don't normally pin anything, but I do pin the borders. Pin the center to the center of the top, pin the quarters to the quarter marks, pin the ends together and then where you may need to ease, work from there.
Then when you put your binding on, hold the layers as you sew.