Hybrid organic–inorganic perovskites (HOIPs) constitute fast-developing class of materials with wide application possibilities. In this study, we investigate two model derivatives of formate HOIPs, acetamidinium manganese(II) formate (AceMn) and formamidinium manganese(II) formate (FMDMn), employing an interdisciplinary approach that combines X-ray diffraction and dielectric spectroscopy under various temperature-pressure conditions. AceMn exhibits atypical pressure-induced structural transformations, including a remarkable phase over-compression exceeding 2 GPa and a phase transition from the ambient-pressure P21/n-symmetric phase II to the higher-symmetry Pbca-symmetric phase III. We have revealed a unique pressure-induced ordering of cage cations in FMDMn, which proceeds without altering the phase symmetry or increasing energy barriers, and its direct relationship with relaxation peak amplitude. Additionally, we have redefined the activation volume parameter and emphasized its role in regulating relaxation dynamics under pressure. Our results indicate that the observed pressure-induced phase transitions within the investigated temperature range result of the combined effect of strain and dynamic of the A-site cation. Our results offer valuable insights for future HOIP research and the design of electronic and optoelectronic devices.