Two possibilities
The instructor was presumably pulling back on the yoke to maintain your airspeed. There are two possible reasons for that:
1. The movement of the rudder had affected the flow over the whole empennage, including the tailplane and elevator, and therefore the hinge moment characteristics of the elevator. The aircraft having manual controls, that might change the force required to hold the elevator in a fixed position. So it would go from no force (with no rudder applied) to some force (with rudder applied). In this case the yoke itself is not moving, but the force changes. I consider this the least likely explanation
2. The rudder movement has induced a pitching moment on the aircraft (either directly or indirectly, see below) which the instructor is counteracting by appling a slightly different elevator angle to maintain the aircraft in trim. In this case the yoke would move in addition to a force being required. The pitching moment may be induced two ways (or some combination of the two):
(a) Directly induced pitching moment. In this case the movement of the rudder creates a pitching moment directly, even if nothing else were to change on the aircraft. This may be due to the location of the forces created by the rudder (side force on the fin and drag on the fin). While the sideforce is unlikely to create a pitching moment (on a single fin aircraft such as this) the drag is unlikely to be acting directly through the aircraft centre of gravity. This will create a pitching moment due to the drag. I consider this unlikely, as it would be more likely to cause a nose-up moment, which would require forward yoke. It is also possible that the flow disturbance of the rudder's movement has created asymmetric flow over the tailplane, which may be creating a pitching moment change. Again, I feel this would be a secondary effect
(b) Indirectly induced pitching moment. In this case it is not the rudder which causes the pitching moment, but the rudder causes something else to change, which is then the source of the pitching moment. If the aircraft were fixed (as in a wind tunnel) there would be no pitching moment here. But with it free to respond to the rudder, there can be. I consider this the most likely explanation What is probably happening is that with application of rudder there is sideslip roduced on the aircraft. It is common for aircraft to have a sensitivity of pitching behaviour to sideslip, due to, among other things, the change in the wing lift as the sweep of the wing is varied relative to the flow.
Hope that helps a bit. Sorry for the "maybes" rather than the definitive answer you were expecting.