The membrane components of cellular organelles have been shown to segregate into domains as the result of biochemical maturation. We propose that the dynamical competition between maturation and lateral segregation of membrane components regulates domain formation. We study a two-component fluid membrane in which enzymatic reaction irreversibly converts one component into another and phase separation triggers the formation of transient membrane domains. The maximum domain size is shown to depend on the maturation rate as a power law similar to the one observed for domain growth with time in the absence of maturation, despite this time dependence not being verified in the case of irreversible maturation. This control of domain size by enzymatic activity could play a critical role in regulating exchange between organelles or within compartmentalized organelles such as the Golgi apparatus.