Thanks to the rapid advances in deep learning techniques and the wide availability of large-scale training sets, the performance of video saliency detection models has been improving steadily and significantly. However, deep learning-based visualaudio fixation prediction is still in its infancy. At present, only a few visual-audio sequences have been furnished, with real fixations being recorded in real visual-audio environments. Hence, it would be neither efficient nor necessary to recollect real fixations under the same visual-audio circumstances. To address this problem, this paper promotes a novel approach in a weakly supervised manner to alleviate the demand of large-scale training sets for visual-audio model training. By using only the video category tags, we propose the selective class activation mapping (SCAM) and its upgrade (SCAM+). In the spatial-temporal-audio circumstance, the former follows a coarse-to-fine strategy to select the most discriminative regions, and these regions are usually capable of exhibiting high consistency with the real human-eye fixations. The latter equips the SCAM with an additional multi-granularity perception mechanism, making the whole process more consistent with that of the real human visual system. Moreover, we distill knowledge from these regions to obtain complete new spatial-temporal-audio (STA) fixation prediction (FP) networks, enabling broad applications in cases where video tags are not available. Without resorting to any real human-eye fixation, the performances of these STA FP networks are comparable to those of fully supervised networks. The code and results are publicly available at https://github.com/guotaowang/STANet.