The series of Cr-chalcogenide spinels ACr₂X₄ (A = Zn, Cd, Hg; X = S, Se) exhibits a rich phase diagram upon compression, as revealed by our recent investigations. There exist, however, some open questions regarding the role of cations in the observed structural transitions. In order to address these queries, we have performed X-ray diffraction and Raman spectroscopic studies on the ZnCr₂S₄ spinel up to 42 GPa, chosen mainly due to the similarity of the Zn²⁺ and Cr³⁺ cationic radii. Two reversible structural transitions were identified at 22 and 33 GPa, into a I4₁/amd and an orthorhombic phase, respectively. Close comparison with the behavior of relevant Cr-spinels revealed that the structural transitions are mainly governed by the competition of the magnetic exchange interactions present in these systems, and not by steric effects. In addition, careful inspection of the starting Fd3m phase revealed a previously unnoticed isostructural transition. The latter is intimately related to changes in the electronic properties of these systems, as evidenced by our Raman studies. Our results provide insights for tuning the physical and chemical properties of these materials, even under moderate compression, as well as promoting the understanding of similar pressure-induced effects in relevant systems.