We show that the pseudo Jahn-Teller effect (PJTE) is instrumental in predicting and rationalizing structural changes in chemical transformations of two-dimensional (2D) molecular systems by means of analyzing the symmetries and electron occupation of the ground and lowest excited electronic states and the energy gap between them, subject to their PJT coupling along the main distortion coordinates. Special attention is paid to rationalizing the PJTE origin of non-planarity of 2D compounds and to the restoration of their planar configurations. Examples of two series of 1,2- and 1,4-dithiin containing tricyclic compounds (carbon sulfide, thianthrene, and antracene and their derivatives) are used to demonstrate in detail the mechanism of (1) enhancement and suppression of the PJTE distortions (puckering) in redox processes, and (2) PJTE induced symmetry breaking and restoration of the planar configuration by chemical substitutions.