An abnormal three-stage martensitic transformation behavior (one-stage R and two-stage B19) has been found in Ni-rich Ti-Ni alloys when aged at intermediate temperatures (350-500℃). This strange behavior was successfully explained by considering the kinetics of Ti3Ni4 precipitation in polycrystalline samples. However, it was found that R-phase transformation occurs in two stages, when aging is done at low temperatures (250-300℃). In order to find the origin of this abnormal phenomenon, we made a comparative study with Ni-49.4 at.% Ti single crystals and polycrystals, which were aged at 250℃ for different time. Differential scanning calorimetry showed that all single crystals undergo normal onestage R-phase transformation, while polycrystals exhibit the abnormal two-stage R-phase transformation after short time aging. These different transformation behaviors can be understood by considering the kinetics of precipitation in supersaturated solid solution. The abnormal two-stage R-phase transformation is attributed to a large-scale heterogeneity of Ni-content between grain boundary region and grain interior, resulted from the preferential precipitation in grain boundary regions. Therefore, it is suggested that there is a unified scenario for seemingly different transformation behaviors of both low-temperature-aged and intermediate-temperature-aged Ti-Ni alloys.