Reservoir inflow prediction is crucial for water resource management, yet existing approaches mainly focus on single-reservoir models that ignore spatial dependencies among interconnected reservoirs. We introduce AdaTrip as an adaptive, time-varying graph learning framework for multi-reservoir inflow forecasting. AdaTrip constructs dynamic graphs where reservoirs are nodes with directed edges reflecting hydrological connections, employing attention mechanisms to automatically identify crucial spatial and temporal dependencies. Evaluation on thirty reservoirs in the Upper Colorado River Basin demonstrates superiority over existing baselines, with improved performance for reservoirs with limited records through parameter sharing. Additionally, AdaTrip provides interpretable attention maps at edge and time-step levels, offering insights into hydrological controls to support operational decision-making. Our code is available at https://github.com/humphreyhuu/AdaTrip.