This video shows how a traditional fast drying carpet cleaning works. Although it's billed as a completely dry cleaning system there is a pre-spray involved in the process. That pre-spray is a wet application and will leave the carpet slightly damp in those areas. This particular fast drying carpet cleaning system is built around a product called Host. It uses what is called cleaning sponges to absorb dirt from the carpet fibers. It does a fairly good job of removing soil from the carpet but unfortunately it does leave a good amount of particulate matter in the carpet.
The cleaning sponges are difficult to remove and only 60-80% of them come out with the final vacuum stage. In Tampa FL that percentage could be higher due to humidity. This photo is from my Chem-Dry carpet cleaning equipment after cleaning a carpet that had previously been cleaned with the fast drying cleaning system shown in the video. You can see all the left over sponges on my cleaning equipment. There was a lot more of it in the waste tank when I cleaned it out at the end of the day.
I highly recommend finding a fast drying carpet cleaner in your area that uses a steam cleaning method of cleaning. Dry cleaning methods that use powders or shaker debris can leave more soil in your carpet than they remove. It might not be visible soils but deep down in the carpet there is an abundance of those small sponges that are difficult to remove. They could hamper future cleanings as well. Consider using a low moisture steam cleaner instead, like Chem-Dry of Tampa.