I recon it's because of 2 effects.
1. while using the rudder there is an amount of movement of air up the rudder which then hits the elevator which then pitches because the trimmer is a spring.
2. It has a relative large rudder and the drag causes a drop in airspeed which causes the nose to drop.
The t-tail does have a few differences compared to the other training air craft due to the fact its away from the prop wash as i am sure you have found out.
BTW personally I think the PA 38 is a fine aircraft for PPL training.