We study context-aware time-series forecasting, in which a single target variable is predicted from its own history and a set of contextual variables, such as weather and calendar information. As the context becomes more diverse, a single model struggles to capture all of its regimes, while ensemble learning and Mixture-of-Experts approaches rely on manual data partitioning or soft routing, which increases the inference cost and hinders interpretability. We propose CATF, a Context-Aware Time-Series Forecasting framework built on a Manager-Worker architecture: a Transformer-based Manager routes each input to a single Worker based on the context, using hard routing during both training and inference. The Workers thus specialize without manual data partitioning, and any single-model forecaster can serve as a Worker. On five context-rich datasets, four horizons, and two normalization schemes, CATF improves over its standalone counterpart in 162 of 200 comparisons, the best CATF-enhanced model outperforms the best standalone baseline in 19 of 20 settings, and it outperforms the zero-shot Time-MoE foundation model in 15 of 20 settings. A case study on bike-sharing data shows that the Manager routes inputs by the calendar and that each Worker specializes in a different weekly pattern.