Dithiazolyl (DTA)-based radicals have furnished many examples of organic spin-transition materials, some of them occurring with hysteresis and some others without. Herein, we present a combined computational and experimental study aimed at deciphering the factors controlling the existence or absence of hysteresis by comparing the phase transitions of 4-cyanobenzo-1,3,2-dithiazolyl and 1,3,5-trithia-2,4,6-triazapentalenyl radicals, which are prototypical examples of non-bistable and bistable spin transitions, respectively. Both materials present low-temperature diamagnetic and high-temperature paramagnetic structures, characterized by dimerized (⋅⋅⋅A-A⋅⋅⋅A-A⋅⋅⋅) and regular (⋅⋅⋅A⋅⋅⋅A⋅⋅⋅A⋅⋅⋅A⋅⋅⋅) π-stacks of radicals, respectively. We show that the regular π-stacks are not potential energy minima but average structures arising from a dynamic inter-conversion between two degenerate dimerized configurations: (⋅⋅⋅A-A⋅⋅⋅A-A⋅⋅⋅) ↔(-A⋅⋅⋅A-A⋅⋅⋅A-) . The emergence of this intra-stack dynamics upon heating gives rise to a second-order phase transition that is responsible for the change in the dominant magnetic interactions of the system. This suggests that the promotion of a (⋅⋅⋅A-A⋅⋅⋅A-A⋅⋅⋅) ↔(-A⋅⋅⋅A-A⋅⋅⋅A-) dynamics is a general mechanism for triggering spin transitions in DTA-based materials. Yet, this intra-stack dynamics does not suffice to generate bistability, which also requires a rearrangement of the intermolecular bonds between the π-stacks via a first-order phase transition.