When I hand sew a binding, this is what I do, the only thing is I don't wait so long to pull the thread through. I find if I wait too long there is a danger of the thread tangling. I think she was just delaying tightening up so the technique could be clear. As far as corners,
- I make sure the side I am sewing down is folded straight out.
- I continue the stitching, to the edge. This leave a sort of triangle on the corner.
- I fold over the next side making sure the edges meet. If the binding was sewn on evenly, this makes a perfect mitered corner.
Hope that makes sense.