They reduce the zooanthelle amount by growing bacteria that consume the N and P allowing the corals to to somewhat starve - starving corals have less diatoms in the tissue and some appear a lot brighter, brown corals have an excess. You can do this with GFO, biopellets, vodka, good husbandry, etc. What this effectively does it makes the carbon based oxic bacteria grow in the zeolite or water column to eat the N and P, instead of in the sand bed where the anoix eat the N and P - and you shift the equilibrium to rely on the product and you are dependent on it. It is hard if you quit because the bacteria that rely on the carbon will die without the food and you have already killed lots of the anoxic bacteria in the sand and it will take months and months for it to repopulate. They have food and aminos and similar stuff that really does not do too much either, but it turns into N and P eventually which does do something.
I ran it for about 18 months in 2008ish, 100% according to the directions, with supplies that I got from a guy who quit the hobby. I can assure you that you can have just as good of colors without it. It isn't snake oil, or anything. The system can work if you follow it. However, it does not do anything that you cannot do without it and accomplish in other ways.
There are tons of threads all over reef central about people who use and love it, as well as people who used it, loved it and now no longer use it anymore and still love their tanks. The one thing that they all have in common is that the individual reefer is self aware and regimented enough to probably make just about any system work.
You can also reach out to the TOTM guys, farmers, fraggers, etc and get their opinions. Some like, some don't, but all have awesome tanks with very good colors.
IMO, there are other factors that you can change to get better color and this might be near the bottom of list if you asked me what to try.