They work on the assumption that organic carbon is in short supply relative to the amount of inorganic phoshorous( PO4) and nitrogen( typically NO3) and that by upping the organic carbon via the carbohydrates in the pellets i bacteria will bloom and consume excess nitrogen and phosphorous. The same occurs with vodka, vinegar, vitamin C, sugar etc.Typically, marine organisms use much more organic carbon than nitrogen and more nitrogen than phosphorous. Ratios vary by organism but a general standard is the redfield ratio at 116 parts organic carbon to 16 parts nitrogen to 1 part phosphate. So it's easy for bacteria to be limited by a lack of organic carbon. Personally, I prefer vodka and vinegar dosing for reasons related to the nature of the anaerobic digestion process and some potential negative consequences from monomers. I'll wait awhile for more experiences with pellets before considering a switch.
When adding extra organic carbon to the tank it's important to pay attention to exporting organics( the bacteria and their by products as well as other organic compounds.) . heavy skimming and granulated activated carbon are helpful. A build up of excess organics can yellow the water and even the non yellowing kind may interfere with coral's symbiont bacteria in a detrimental way.