Transmission interface power flow adjustment is a critical measure to ensure the security and economy operation of power systems. However, conventional model-based adjustment schemes are limited by the increasing variations and uncertainties occur in power systems, where the adjustment problems of different transmission interfaces are often treated as several independent tasks, ignoring their coupling relationship and even leading to conflict decisions. In this paper, we introduce a novel data-driven deep reinforcement learning (DRL) approach, to handle multiple power flow adjustment tasks jointly instead of learning each task from scratch. At the heart of the proposed method is a multi-task attribution map (MAM), which enables the DRL agent to explicitly attribute each transmission interface task to different power system nodes with task-adaptive attention weights. Based on this MAM, the agent can further provide effective strategies to solve the multi-task adjustment problem with a near-optimal operation cost. Simulation results on the IEEE 118-bus system, a realistic 300-bus system in China, and a very large European system with 9241 buses demonstrate that the proposed method significantly improves the performance compared with several baseline methods, and exhibits high interpretability with the learnable MAM.