Distantly-Supervised Named Entity Recognition (DS-NER) effectively alleviates the data scarcity problem in NER by automatically generating training samples. Unfortunately, the distant supervision may induce noisy labels, thus undermining the robustness of the learned models and restricting the practical application. To relieve this problem, recent works adopt self-training teacher-student frameworks to gradually refine the training labels and improve the generalization ability of NER models. However, we argue that the performance of the current self-training frameworks for DS-NER is severely underestimated by their plain designs, including both inadequate student learning and coarse-grained teacher updating. Therefore, in this paper, we make the first attempt to alleviate these issues by proposing: (1) adaptive teacher learning comprised of joint training of two teacher-student networks and considering both consistent and inconsistent predictions between two teachers, thus promoting comprehensive student learning. (2) fine-grained student ensemble that updates each fragment of the teacher model with a temporal moving average of the corresponding fragment of the student, which enhances consistent predictions on each model fragment against noise. To verify the effectiveness of our proposed method, we conduct experiments on four DS-NER datasets. The experimental results demonstrate that our method significantly surpasses previous SOTA methods. The code is available at https://github.com/zenhjunpro/ATSEN.