Continuous sign language recognition (CSLR) requires precise spatio-temporal modeling to accurately recognize sequences of gestures in videos. Existing frameworks often rely on CNN-based spatial backbones combined with temporal convolution or recurrent modules. These techniques fail in capturing fine-grained hand and facial cues and modeling long-range temporal dependencies. To address these limitations, we propose the Unified Spatio-Temporal Modeling (USTM) framework, a spatio-temporal encoder that effectively models complex patterns using a combination of a Swin Transformer backbone enhanced with lightweight temporal adapter with positional embeddings (TAPE). Our framework captures fine-grained spatial features alongside short and long-term temporal context, enabling robust sign language recognition from RGB videos without relying on multi-stream inputs or auxiliary modalities. Extensive experiments on benchmarked datasets including PHOENIX14, PHOENIX14T, and CSL-Daily demonstrate that USTM achieves state-of-the-art performance against RGB-based as well as multi-modal CSLR approaches, while maintaining competitive performance against multi-stream approaches. These results highlight the strength and efficacy of the USTM framework for CSLR. The code is available at https://github.com/gufranSabri/USTM