I don't know the aero theory for the pitch down moment
Although a specific Type might have a specific reason .. the general story is
(a) tailplane provides a noseup pitch (ie download) for balance
(b) depending on fuselage airflow in sideslip the lee tailplane surface can see disrupted airflow ("blanketing") and a reduction in downforce overall
(c) result is a nose down pitch
Sometimes this is more evident with flap extended (eg some Cessnas)