Out-of-distribution (OOD) detection discerns OOD data where the predictor cannot make valid predictions as in-distribution (ID) data, thereby increasing the reliability of open-world classification. However, it is typically hard to collect real out-of-distribution (OOD) data for training a predictor capable of discerning ID and OOD patterns. This obstacle gives rise to data generation-based learning methods, synthesizing OOD data via data generators for predictor training without requiring any real OOD data. Related methods typically pre-train a generator on ID data and adopt various selection procedures to find those data likely to be the OOD cases. However, generated data may still coincide with ID semantics, i.e., mistaken OOD generation remains, confusing the predictor between ID and OOD data. To this end, we suggest that generated data (with mistaken OOD generation) can be used to devise an auxiliary OOD detection task to facilitate real OOD detection. Specifically, we can ensure that learning from such an auxiliary task is beneficial if the ID and the OOD parts have disjoint supports, with the help of a well-designed training procedure for the predictor. Accordingly, we propose a powerful data generation-based learning method named Auxiliary Task-based OOD Learning (ATOL) that can relieve the mistaken OOD generation. We conduct extensive experiments under various OOD detection setups, demonstrating the effectiveness of our method against its advanced counterparts.