I'm sure there are many factors which induce the spin, but the most simple model that I can imagine is where you have a surface with a center of drag that is not coaxial with the pivot point. The aerodynamic forces push the mass away from the vertical. When gravity tries to restore the mass to the vertical, the drag force in the lateral plane couples with the lateral component of the restoring force to create a spinnning moment. Initially, this couple is unstable in direction of rotation, but once the spinning starts this couple becomes very stable and can rapidly increase the rate of spinning. A picture is worth a thousand words here.
If you're not convinced, go fishing. Spinners and spoons do the same thing when pulled through the water. As an experiment, tie any object from flat plates, to army men onto a piece of string and pull them through water in your bath tub. When moving slowly, there is a little dance that results in movement lateral to the string and some rotation. When pulled quickly enough, a spin can easily develop.
Since this model only requires linear flow it implies that the same can happen under a coaxial.
To stop the spinning, you could proactively get rid of the cause or reactively get rid of the spin. Balancing the drag would be difficult, but may result in some success. Active surfaces may help but would increase mass, complexity and could aggravate a spin. A two line system with both lines coming from the helicopter would work to an extent, but would increase the risk of snagging in trees and comes with a dangerous result from a line failure (potentially less dangerous than using a single line, but something to consider).
I've seen many people develop very fast spin rates in short times. Putting them back on the ground, back in the water, or holding them just underneath the helicopter tends to fix the problem. However, if there is a critical casualty also on the line, the spinning is an additional trauma that could make a huge difference in the success of the rescue.
Matthew.