Aggregated time series are widely used in business and economics, where top-level sequences (e.g., category sales) aggregated from underlying sequences (e.g., individual items) often exhibit clearer trends and are therefore typically the primary focus of forecasting tasks. However, treating top-level sequences as ordinary multivariate time series is inappropriate in the presence of coupled aggregation constraints. The core challenge arises in coupled aggregation structures, where a single underlying sequence contributes to multiple top-level sequences, as simple nonnegativity constraints of underlying sequences induce highly complex constraints among top-level sequences. Existing methods fail to achieve high accuracy while satisfying these constraints. To address this, we propose ProCAST, a projection-based framework that adjusts forecasts from any multivariate base model to satisfy coupled aggregation constraints. By introducing virtual underlying sequences and leveraging orthogonal and oblique projection, our method ensures that the top-level forecasts are feasible without explicitly deriving complex constraints. Theoretically, we prove that the proposed method guarantees improved accuracy under distance-based loss functions. Experiments on real-world datasets show that our method completely eliminates constraint violations while achieving higher accuracy than current state-of-the-art approaches.