Kinetic Monte Carlo (KMC) simulations of the diffusion couple experiments were performed with the assumption that the vacancy composition in the system equilibrates much faster than the atomic configuration. Within this approach, the consistent atomistic simulation model with immediate vacancy equilibration mechanism was developed by incorporating a physical model of vacancy sources and sinks into the KMC algorithm. The Semi-Grand Canonical Monte Carlo (SGCMC) algorithm determined equilibrium vacancy composition and configuration in a system and, when implemented with the KMC code, generated on-line vacancy compositions locally equilibrated according to the atomic configuration in the sample. The values of the interdiffusion coefficients were determined by means of the Boltzmann-Matano formalism applied to the simulated composition profiles along the diffusion couple. The simulations also clearly reproduced the Kirkendall effect expected to appear in the simulated systems. Validity and reliability of the approach was assessed by comparing the results with the predictions of the Darken-Manning theory.