For me ... whether it's a tablre runner or a full size quilt ....
Square first before quilting ... then square again after quilting.
If you leave it all til after, you run too much of a risk to having to cut some of your quilting off as you square up.
Plus if there's any serious problems, (eg. border not laying totally flat, and needing to restitch a seam to get it to flat and square, etc.) you can get that sorted out before quilting ... when it's possible to correct. After quilting ... it's way to late!