You probably are talking about the TuckUnder effect. There are several factors causing it. The main one is that as airflow separation takes place, the downwash behind the wing is decreased. Prior to this, the horizontal stabilizer is trimmed to keep the airplane level. With this decrease in downwash, the stabilizer AOA, in effect, is increased thus pushing the tail up hence the pitch down.
There are two other factors. One is that as the shock waves move rearward, so is the center of pressure, adding to the tuckunder. The second is that, as Seagull said, is the aerodynamic center shifts rearward, adding to the Tuckunder effect. One interesting about the aerodynamic center shift is that in some aircraft, the aero center shift forward first (causing momentary pitch up) before eventually shifts rearward (pitch down). this was probably what CULBER was thinking about.
All aircraft flying supersonically suffer a nose down pitching moment.