Online Action Detection (OAD) detects actions in streaming videos using past observations. State-of-the-art OAD approaches model past observations and their interactions with an anticipated future. The past is encoded using short- and long-term memories to capture immediate and long-range dependencies, while anticipation compensates for missing future context.We uncover a training-inference discrepancy in existing OAD methods that hinders learning effectiveness. The training uses varying lengths of short-term memory, while inference relies on a full-length short-term memory. As a remedy, we propose a Context-enhanced Memory-Refined Transformer (CMeRT). CMeRT introduces a context-enhanced encoder to improve frame representations using additional near-past context. It also features a memory-refined decoder to leverage near-future generation to enhance performance.CMeRT improves learning for OAD and achieves state-of-the-art in online detection and anticipation on THUMOS'14, CrossTask, and EPIC-Kitchens-100.