The psychologist Peter Dowrick spent decades studying how people learn by watching themselves. He called it self-modeling: when you see or hear yourself doing something a little better than you usually do, it shows you what you can already do, and you learn it quickly. His review 'Self model theory: learning from the future' (2012) brings that work together.
WillpowerLab uses the same idea. Your most confident moments are kept, so you can hear what your confident voice already sounds like.
Judging is our own addition to it. When you listen to a recording and answer one question, 'Does this sound confident to you?', you train your ear to notice confidence, in other voices and in your own. Honest answers sharpen that ear; kind answers that aren't true blur it. The clearer you can hear a confident voice, the less room is left for the inner critic.
Reference: Dowrick, P. W. (2012). Self model theory: learning from the future. WIREs Cognitive Science, 3(2), 215–230.