No, all the borders are usually put on before quilting. Just a couple of questions -
Did you quilt equally in the center and borders? Quilting shrinks up the quilt a bit, so if the borders aren't quilted as heavily as the center then they will flare.
Were the borders wavy before you started quilting? This is a common problem.
Are you pulling on the sides of the quilt a lot while quilting it? You might be stretching the fabric that way.
Is it possible that the fabric on the edges is on the bias? (Unlikely, but that could also cause stretched-out borders.)
That's all I can think of. Maybe someone else will have more ideas. What kind of frame are we talking about? I assume it's for machine quilting?