Major depressive disorder (MDD) is a common neuropsychiatric condition whose accurate diagnosis from resting-state functional magnetic resonance imaging (rs-fMRI) remains difficult. Dynamic functional connectivity (DFC) captures time-varying interactions among brain regions and provides rich spatio-temporal information, yet current DFC-based methods face three limitations: sliding-window Pearson correlation yields noisy estimates sensitive to window length and motion artifacts; correlation-derived node features do not fully exploit frequency-domain properties of blood-oxygen-level-dependent (BOLD) signals; and most spatio-temporal graph models handle spatial structure and temporal dynamics in separate stages, restricting their ability to represent coupled brain network evolution. To overcome these issues, we reformulate DFC learning as joint spatio-temporal graph representation learning under a Hawkes-process-inspired temporal dependency prior and propose HWSTCL, a two-stage framework built on a reliability-refined joint spatio-temporal graph with a kernel-weighted pretraining objective. Within each temporal window, BOLD signals are encoded as spectral node descriptors and functional edges are refined by an exponential distance-decay prior that down-weights less reliable long-range connections. The joint graph is then formed by linking each region to itself across future windows through a Hawkes-inspired exponential kernel, allowing spatial and temporal information to be propagated together during message passing. A kernel-weighted contrastive objective further promotes temporal consistency for each region across windows while reducing redundant similarity between different regions. Experiments on a benchmark rs-fMRI dataset show that HWSTCL outperforms recent baselines and yields coherent spatio-temporal representations for MDD diagnosis.