Running multi-task DNNs on mobiles is an emerging trend for various applications like autonomous driving and mobile NLP. Mobile DNNs are often compressed to fit the limited resources and thus suffer from degraded accuracy and generalizability due to data drift. DNN evolution, e.g., continuous learning and domain adaptation, has been demonstrated effective in overcoming these issues, mostly for single-task DNN, leaving multi-task DNN evolution an important yet open challenge. To fill up this gap, we propose AdaBridge, which exploits computational redundancies in multi-task DNNs as a unique opportunity for dynamic data and computation reuse, thereby improving training efficacy and resource efficiency among asynchronous multi-task co-evolution in edge systems. Experimental evaluation shows that AdaBridge achieves 11% average accuracy gain upon individual evolution baselines.