Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End-functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regimes for small reactant concentrations rho(0) R-g(3) = 0.0406-0.163. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a root t-law is observed in the intermediate stage.