Magnetic bistability in organic-radical based materials has attracted significant interest due to its potential application in electronic devices. The first-principles bottom-up study herein presented aims at elucidating the key factors behind the different magnetic response of the low and high temperature phases of four different switchable dithiazolyl (DTA)-based compounds. The drastic change in the magnetic response upon spin transition is always due to the changes in the JAB magnetic interactions between adjacent radicals along the π-stacks of the crystal, which in turn are driven mostly by the changes in the interplanar distance and degree of lateral slippage, according to the interpretation of a series of magneto-structural correlation maps. Furthermore, specific geometrical dispositions have been recognized as a ferromagnetic fingerprint in such correlations. Our results thus show that an appropriate substitution of the chemical skeleton attached to the DTA ring could give rise to new organic materials with dominant ferromagnetic interactions.