Vacancy-mediated self-diffusion and chemical ordering in B2 ordering triple-defect binary intermetallics was modelled with Ising nn and nnn pair interactions and simulated in atomistic scale. The Kinetic Monte Carlo (KMC) algorithm was implemented with local-configuration-dependent migration barriers and temperature-dependent equilibrium vacancy concentration determined by means of Semi Grand Canonical Monte Carlo (SGCMC) simulations. The resulting concentration dependence of the component tracer diffusivities in a triple-defect B2-ordering A-B system mimicking Ni-Al was in a very good agreement with the experimental results obtained for that system. In particular, inversion of the relationship between the Ni and Al-diffusivities in Al-rich Ni-Al systems deduced from the features of interdiffusion in Ni-Al was perfectly reproduced by direct self-diffusion simulations. The origin of the phenomenon is elucidated in terms of an increase of the nnn Al jump frequency caused by the generation of structural Ni-vacancies.