The abrupt onset of breathing pressure is excessively overdone in the video. In fact, pressure builds up continuously from zero. But this doesn't change the basic result either: an initial oscillation fades away, leaving a constant bend.
Vividly: a constant force can cause the blues harp reed momentarily to vibrate by "pushing", but this vibration disappears again.
How can a continuing strong vibration of the reed nevertheless occur? The answer will be: feedback!