Efficient acquisition, storage, and utilization of traffic data are critical challenges in spatio-temporal data management. Most traffic data systems collect and store observations at fixed, coarse-grained temporal intervals to reduce storage and computation costs. However, such coarse-grained data severely limits downstream applications that require predictions at a finer temporal granularity. Collecting and maintaining fine-grained traffic data across all locations and time periods would impose a substantial burden on database storage and preprocessing pipelines. To address this temporal granularity mismatch, we formulate a novel problem: predicting fine-grained future traffic using coarse-grained sampled data. We propose the Spatial-Temporal Refinement Predictor (STRP), a granularity-aware framework for spatio-temporal data systems. STRP integrates two components: Tree Convolution for efficient and interpretable spatial dependency modeling, and Inverse Dilated Convolution for progressive temporal extrapolation. STRP supports two practical prediction settings: window-based and duration-based, to handle different forms of granularity mismatch. Experiments on six benchmark datasets show that STRP significantly outperforms state-of-the-art baselines in both accuracy and efficiency. Our work offers a practical and interpretable approach to managing granularity mismatches in spatio-temporal traffic data systems.