Using density-functional-theory-based calculations, we explore the factors that influence the phase stability of Ni and Mn excess off-stoichiometric Ni2MnSb alloys which have lately been proven to possess properties important for state-of-the art technology. Our calculations and subsequent analysis of the electronic structures pinpoint the origin of the behavior of phase stability in Ni-Mn-Sb systems. We find that the site occupancy patterns and subsequent magnetic structures are the key toward effecting a martensitic phase transformation. Our results demonstrate that apart from Ni2Mn1+xSb1-x, systems which have been experimentally observed to possess magnetic shape memory effect, Ni2+xMnSb1-x, too are potential shape memory alloys where an unexpected site occupancy configuration leading to reduction of total energy drives the martensitic phase transformation. This, thus, opens more possibilities for the experimentalists to explore new materials for magnetic shape memory and associated functional effects. The systems, irrespective of composition, are found to be ductile, a necessity for practical applications.