The present study deals with diffusion behavior of adsorbed atoms on stepped crystal surfaces. In volume-immiscible systems, two-dimensional (2D) atomic intermixing at epitaxial interface could be completely blocked on step-free surface domains. This is a result of high diffusion barrier for direct atomic exchange between adsorbed layer and substrate. In that case, diffusion takes place exclusively across the steps of atomic terraces. In such systems, dynamic competition between energy gain by mixing and substrate strain energy results in diffusion scenario where adsorbed atoms form alloyed stripes in the vicinity of terrace edges. At high temperatures, the stripe width increases and finally completely destroys the terraces. This process leads to formation of alloyed 2D atomic islands on top of pure substrate layer. The atomistic Monte Carlo simulations reveal vacancy-mediated mechanism of diffusion inside atomic terraces as a result of spontaneous generation of vacancies at high temperature. Being in agreement with recent experimental findings, the observed surface-confined alloying opens up a way various surface pattern to be configured at different atomic levels on the crystal surface.