After aging at intermediate temperatures (400-500℃), Ni-rich Ti-Ni alloys undergo an abnormal 3-stage martensitic transformation behavior (1-stage R and 2-stage B190), which stems from a preferential Ti3Ni4 precipitation around grain boundary. On the other hand, if aged at low-temperatures (250-300℃), they undergo 2-stage R-phase transformation, but the origin of this strange phenomenon is unclear. In the present study, we made a systematic study of this phenomenon by considering the grain boundary effect and composition effect. We found that all single crystals undergo 1-stage R-phase transformation; in contrast, the transformation behavior of polycrystals is dependent on Ni content: low-Ni (50.6Ni, 51Ni) polycrystals undergo 2-stage R-phase transformation while high-Ni (52Ni) polycrystals undergo 1-stage R-phase transformation. The abnormal 2-stage R-phase transformation is attributed to a large-scale compositiona lheterogeneity in B2 matrix between grain boundary region and grain interior, due to the heterogeneity in precipitate density between the grain boundary and grain interior. But for high-Ni polycrystals, precipitates are essentially homogeneously distributed across the whole grain and this leads to normal 1-stage R-phase transformation. The different transformation behavior of low-Ni and high-Ni polycrystals stems from a competition between two opposing tendencies: (1) for preferential precipitation in the grain boundary; (2) for homogeneous precipitation across the whole grain with high-Ni content. The difference between the effect of intermediate-temperature and low-temperature aging lies in the difference in the ability for long-range diffusion of Ni (from the grain interior to the grain boundary), which results in whether or not Ti3Ni4 precipitates can form in the grain interior. Our results lead to a unified explanation for different transformation behaviors of both low-temperature and intermediate-temperature aged alloys in terms of the kinetics of precipitation in supersaturated polycrystals.