Start stitching (and backstitch) on that same point where you stopped before, at the center diagonal of the corner and 1/4" away from the raw edge.
This is mostly for me, but here's how I did the 120° corners on the mini quilt/tablerunner. Mark a diagonal line at the corner and stop stitching on or just shy of that point. Make sure and backstitch.
This step is where we see the biggest difference in applying binding to 90° corners, when you fold the binding back over itself- align the raw-edge bottom of the binding straight with the bottom edge of the next section around the corner you're working on of the item being bound.
Some closeups of how the binding looks.