Uncertainty quantification is crucial for many safety-critical applications. Evidential Deep Learning (EDL) has been demonstrated to provide effective and efficient uncertainty estimates on well-curated data. Yet, the effect of class imbalance on performance remains not well understood. Since real-world data is often represented by a skewed class distribution, in this paper, we holistically study the behaviour of EDL, and further propose Hybrid-EDL by integrating data over-sampling and post-hoc calibration to boost the robustness of EDL. Extensive experiments on synthetic and real-world healthcare datasets with label distribution skew demonstrate the superiority of our Hybrid-EDL, in terms of in-domain categorical prediction and confidence estimation, as well as out-of-distribution detection. Our research closes the gap between the theory of uncertainty quantification and the practice of trustworthy applications.