While pressure-induced changes in the electronic, magnetic, and optical properties of Cu-Cl hybrid perovskites have been studied intensively, the correlation between these properties and pressure-induced structural changes is still vaguely understood. Here, by first-principles calculations on a model system (EDBE)[CuCl4] (EDBE = 2,2'-(ethylenedioxy)bis(ethylammonium)) (a Cu-Cl hybrid perovskite), we correlate the evolution of a series of exciting physical properties with pressure while resolving some of the long-standing debates on the fundamental electronic nature of this important class of material. The material shows two structural phase transitions and an anisotropy in compressibility with increasing pressure. After a critical pressure of 17 GPa, the structure becomes highly symmetric, thereby suppressing the Jahn-Teller distortions. At zero pressure, mapping the optical transitions with the Laporte selection rules, lower and higher energy excitations are found to be of Mott-Hubbard (MH) and charge transfer (CT) type, respectively, signifying the material to be a Mott insulator. The material shows a red shift in the charge transfer band edge with increasing pressure and temperature, demonstrating the piezochromism and the thermochromism, respectively. Piezochromism originates from the changes in mixing of Cl-Cu p-d states, while thermochromism is due to broadening of conduction band states, thereby showing different electronic and structural evolution with pressure and temperature. Furthermore, the magnetic ordering in the material was found to be stable up to higher pressures, making pressure a tool to tune the electronic property without perturbing the magnetic property.