The transformation of potassium bromide from the B1 to the high-pressure B2 structure type is investigated by means of molecular dynamics simulations and compared to previous studies of KF and KCl. The underlying simulation scheme is based on the transition path sampling approach, which allows an unbiased investigation of the phase transition and offers a unique perspective for studying the involved mechanisms at the atomistic level of detail. Our analysis reveals identical mechanisms for the overall transition in KF, KCl, and KBr, but rather dissimilar characteristics of the nucleation and growth of phases. The transformation of KCl may be initiated by both K+ and Cl-ion displacement, exhibiting no preference for either species. However, for KF and KBr, we identified a clear favoring of column-wise F- and K+ displacement, respectively. Such tendencies have important implications on the morphogenesis of the phase nuclei and account for the observation of short-ranged coexisting nucleation centers, resulting in the formation of nanosized twin domains separated by mirror planes on completion of the transition. On the basis of a systematic study of potassium halides, we present a conclusive explanation for the observed nucleation characteristics, which is expected to be of general relevance to pressure-induced phase transitions in ionic compounds.