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⋅⋅⋅)n and regular (⋅⋅⋅A⋅⋅⋅A⋅⋅⋅A⋅⋅⋅A⋅⋅⋅)n 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⋅⋅⋅)n↔(‐A⋅⋅⋅A−A⋅⋅⋅A‐)n. 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⋅⋅⋅)n↔(‐A⋅⋅⋅A−A⋅⋅⋅A‐)n 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.