In the past, when sewing with elastic thread (in the bobbin only) there was no need to pull to gather. The elastic thread almost makes the fabric smocked, with stretch. If you were to pull the elastic you would lose some stretch. If you were to pull the top thread you'd cut into the elastic thread.

If you get your tension set correctly the elastic stretches as it feeds through the bobbin and then relaxes when done and this gathers the fabric. I would be a bit concerned that only 3 lines of stitching is supposed to form the waist of a skirt. I'm not sure that is going to be strong enough to hold it in place.