My take on it:
As the aircraft banks, the lift vector, staying perpendicular to the wings, is tilted. This resolves into two components. A vertical component, counteracting the weight of the aircraft, and a horizontal component, giving a centripetal force that pushes the aircraft sideways into a turn. Since the vertical component is initially smaller than the weight, it must be increased by use of elevator to keep the aircraft level. As the plane rolls into the bank, two sources of yaw develop. The first is to yaw into the turn, caused by the flow of air on the fin tending to want to weathercock the aircraft. The second is the adverse aileron yaw, caused by the lowered aileron on the raised wing slowing that wing down more than the lower wing, thus causing the plane to yaw away from the turn. Adverse aileron yaw is usually greatest, so rudder must be applied to cancel it out. Thus, in a balanced turn, there is no slip force in either direction, since centripetal and centrifugal forces are balanced. In an unbalanced turn, then under-rudder allows a slip force which skids the plane out, and over-rudder causes a slip force which yaws the plane into the turn. These forces are present throughout the turn - not just in the initial roll - so rudder must be applied throughout to remain in balance.
Does that sound right?