So as I understand it (basically), when you apply booster or speed glue for that matter, the chemicals expand the sponge. This increases the energy efficiency of the sponge which mostly impacts speed, softens the sponge increasing the feeling, and stretches out the top sheet. The third point is the most important, creating the backwards dome (the rubber is being curled back under the force of the expansion). The stretching of the top sheet is like a spring or tight rope so when a ball interrupts it it springs back harder creating more spin and speed. I was skeptical about boosting for a while, as I was beginning and didn't feel the speed would help. But the spin gave me much more confidence in landing shots and the softening of the sponge made me at least perceive I had more control and feeling. As a short note, I've always preferred nonboosted tackies for service as you can more easily keep the ball short and spinny. But it's marginal nothing close to the benefits of opening loops, loop drives, drives, blocks that boosting provides.
Please do correct me if you have better information. This is mostly anecdotal.