We investigate the spacetime evolution of spin polarization within a hydrodynamic framework based on the de Groot--van Leeuwen--van Weert expressions for energy-momentum and spin tensors. The system's deviation from boost invariance results in the interplay of different spin polarization components, impacting spin observables. We specifically examine the transverse momentum, azimuthal angle, and rapidity dependence of the mean spin polarization vector of $\Lambda$ hyperons. Our results qualitatively align with other models and experimental data on global spin polarization rapidity dependence. While the quadrupole structure is absent in the longitudinal component at midrapidity, our analysis reveals non-trivial signal at forward rapidities that differs from predictions based on the Bjorken expansion.