Understanding the heterogeneous nano/microscopic structures of various organic glasses is fundamental and necessary for many applications. Recently, unusual structural phenomena have been observed experimentally in various organic glasses near their glass transition temperatures (Tg), including dibutyl phthalate (DBP). In particular, the librational motion of radical probe in the glass is progressively suppressed upon temperature increase. In this work, we report in-depth molecular dynamics studies of structural anomalies in DBP glass, that revealed insights into the general mechanism of these phenomena. In particular, we have evidenced that the two types of solvation within alkyl chains coexist, allowing only small-angle wobbling of the solute molecule (TEMPO radical), and another favouring large-angle rotations. The former solvation assumes constrained location of the solute near carboxyl groups of DBP, while the latter is coupled to the concerted movement of butyl chains. Remarkably, excellent qualitative and quantitative agreement with previous experimental results were obtained. As such, we are certain that the above-mentioned dynamic phenomena explain the intriguing structural anomalies observed in DBP and some other glasses in the vicinity of Tg.