Emotion recognition using electroencephalogram (EEG) mainly has two scenarios: classification of the discrete labels and regression of the continuously tagged labels. Although many algorithms were proposed for classification tasks, there are only a few methods for regression tasks. For emotion regression, the label is continuous in time. A natural method is to learn the temporal dynamic patterns. In previous studies, long short-term memory (LSTM) and temporal convolutional neural networks (TCN) were utilized to learn the temporal contextual information from feature vectors of EEG. However, the spatial patterns of EEG were not effectively extracted. To enable the spatial learning ability of TCN towards better regression and classification performances, we propose a novel unified model, named MASA-TCN, for EEG emotion regression and classification tasks. The space-aware temporal layer enables TCN to additionally learn from spatial relations among EEG electrodes. Besides, a novel multi-anchor block with attentive fusion is proposed to learn dynamic temporal dependencies. Experiments on two publicly available datasets show MASA-TCN achieves higher results than the state-of-the-art methods for both EEG emotion regression and classification tasks. The code is available at https://github.com/yi-ding-cs/MASA-TCN.