The interesting part about this is that it is a chain of events all linked together. When doing multiple spins, the guy becomes a support layer and a driving layer. He continues to give you the same momentum you require to continue spinning by making concentric circles around your head (or in your specific 'spinning zone'). But for this to happen, you first spin is very important. The first spin should be the fastest spin because it sets the initial power and carried momentum for the rest of the spins. Additionally, if you are off balance during your first spin, it is a high probability that the rest of your time spinning will be trying to recover from your first spin.
However, to perform that first spin correctly, you need a good prep. The prepping (setup) involves the lady knowing exactly where her center of balance is and having good core (having strong abs help). In addition having good frame and firmness in the arms is essential to keeping a good frame while spinning as well as using any free hands for stability and balance throughout the spins. Also, keeping the knees a little bent will help them with the balance throughout the spins as well. I think the prep is the most important thing - and the followers (ladies) should be practicing prepping as often as they practice spinning. You should practice prepping to the point where you don't even think about prepping. It should be an automatic position that when the guy leads a double or triple spin, you are already in place ready to go.