You should have made a little flap when cutting the slit across, so fold the bottom half down. Insert the unfinished bottom side of the welt into said hole, and on the reverse, line up the folded over flap with the bottom of the welt. They should be right sides together. You can pin if you like, but there's one more piece before sewing in — the pocket liner! Cut out a piece of the fabric for the pocket liner, the same width as the finished welt (the openable part of the pocket will be about 0.5" in on each side, so that will still give you seam allowance). Height should be about 2x depth of your pocket + 0.5" for seams. Now, looking at the back of the welt, from the wrong side of the vest, unfold the liner, and face together the "right" side of the liner (to show inside the pocket), with the pocket / inside of the welt.
With the vest upright, and wrong side facing you, you should basically have the pocket liner face down, with the bottom lined up with the bottom of the welt.