In the hydrocarbon pool mechanism, methanol or dimethyl ether (DME) initially reacts on the catalyst surface to form primary hydrocarbons like ethylene and propylene. These primary products then further react to generate a pool of hydrocarbons within the catalyst's porous structure. The hydrocarbon pool serves as a reservoir that continuously interacts with incoming methanol or DME, leading to a series of reactions that produce a wide range of hydrocarbons.