Well, as you probably know, I'm more of a social dancer than a performer. Not that I don't like performing, but I think most of the 'magic' in salsa happens on the dancefloor when you are social dancing and playing with your partner. This is two dancers playing with the music and having fun in Melody Santorico. Now, I'd like you to pay attention at the spinners (and even the guys spinning) how they are very fluid and effortless. When dancing with a good spinner, they will handle their own balance and control. All the guy has to do is put in the extra little effort to 'continue' the momentum that was started in their first turn. When doing multiple spins with the lady, there are two main important things to make those spins work: the prep, and the first spin. If either of those is not done right, spinning multiple times will be a disaster (unless you have a magical follower or lead that can recover very well).
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.