In driving scenarios, automobile active safety systems are increasingly incorporating deep learning technology. These systems typically need to handle multiple tasks simultaneously, such as detecting fatigue driving and recognizing the driver's identity. However, the traditional parallel-style approach of combining multiple single-task models tends to waste resources when dealing with similar tasks. Therefore, we propose a novel tree-style multi-task modeling approach for multi-task learning, which rooted at a shared backbone, more dedicated separate module branches are appended as the model pipeline goes deeper. Following the tree-style approach, we propose a multi-task learning model for simultaneously performing driver fatigue detection and face recognition for identifying a driver. This model shares a common feature extraction backbone module, with further separated feature extraction and classification module branches. The dedicated branches exploit and combine spatial and channel attention mechanisms to generate space-channel fused-attention enhanced features, leading to improved detection performance. As only single-task datasets are available, we introduce techniques including alternating updation and gradient accumulation for training our multi-task model using only the single-task datasets. The effectiveness of our tree-style multi-task learning model is verified through extensive validations.