Joint-Embedding Predictive Architecture (JEPA) is increasingly used for visual representation learning and as a component in model-based RL, but its behavior remains poorly understood. We provide a theoretical characterization of a simple, practical JEPA variant that has an auxiliary regression head trained jointly with latent dynamics. We prove a No Unhealthy Representation Collapse theorem: in deterministic MDPs, if training drives both the latent-transition consistency loss and the auxiliary regression loss to zero, then any pair of non-equivalent observations, i.e., those that do not have the same transition dynamics or auxiliary value, must map to distinct latent representations. Thus, the auxiliary task anchors which distinctions the representation must preserve. Controlled ablations in a counting environment corroborate the theory and show that training the JEPA model jointly with the auxiliary head generates a richer representation than training them separately. Our work indicates a path to improve JEPA encoders: training them with an auxiliary function that, together with the transition dynamics, encodes the right equivalence relations.