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Three-dimensional organic-inorganic perovskites are rapidly evolving materials with diverse applications. This study focuses on their two representatives - acetamidinium manganese(II) formate (AceMn) and formamidinium manganese(II) formate (FMDMn) - subjected to varying temperature and pressure. We show that AceMn undergoes atypical pressure-induced structural transformations at room temperature, increasing the symmetry from ambient-pressure P2 1 /n phase II to the high-pressure Pbca phase III. In turn, FMDMn in its C2/c phase II displays temperature- and pressure-induced ordering of cage cations that proceeds without changing the phase symmetry or energy barriers. The FMD + cations do not order under constant volume across the pressure-temperature plane, despite similar pressure and temperature evolution of the unit-cell parameters. Temperature and pressure affect the cage cations differently, which is particularly pronounced in their relaxation dynamics seen by dielectric spectroscopy. Their motion require a rearrangement of the metal-formate framework, resulting in the energy and volumetric barriers defined by temperature-independent activation energy and activation volume parameters. As this process is phonon-assisted, the relaxation time is strongly temperature-dependent. Consequently, relaxation times do not scale with unit-cell volume nor H-bond lengths in formates, offering the possibility of tuning their electronic properties by external stimuli (like temperature or pressure) even without any structural changes., (© 2024. The Author(s).)