Spatiotemporal mode locking is a nonlinear process of multimode soliton self-organization. Here the real-time buildup dynamics of the multiple solitons in a spatiotemporal mode-locked multimode fiber laser are investigated, assisted by the time-stretch technique. We find that the buildup processes are transverse mode dependent, especially during the stages of relaxation oscillation and Q-switching prior to multiple soliton formation. Furthermore, we observe that the transverse modal composition of these generated pulses among the multiple solitons can be different from each other, indicating the spatiotemporal structure of the multiple soliton. A simplified theoretical model based on pulse energy evolution is put forward to interpret the role of 3D saturable absorber on spatiotemporal structures of spatiotemporal mode-locking multiple solitons. Our work has presented the spatiotemporal nonlinear dynamics in multimode fiber lasers, which are novel to those inside the single transverse mode fiber lasers.