Spatiotemporal (4D) atlases of fetal brains are essential for quantitative analysis of the dynamic morphological changes and developmental patterns of the prenatal brain. An essential step in atlas construction is image registration, wherein accurate alignment of anatomical structures across subjects is essential for generating meaningful atlases. In existing learning-based atlas construction frameworks, registration is mainly driven by the matching of intensity images. However, due to the inherently low and spatiotemporally varying tissue contrasts and dynamic gyrification during prenatal brain development, enforcing anatomical constraints solely via intensity images often leads to inaccurate alignment, especially for the complex, folded cortical regions. To address this issue, we propose a novel learning-based framework which leverages accurate inter-subject cortical anatomical correspondences established by surface registration to improve deformation predictions. The proposed method leads us to construct continuous, high-quality, and anatomically meaningful 4D volumetric atlases. Specifically, given gestational age (GA) and two randomly selected subjects at this GA, the atlas synthesis network generates an atlas based on the input GA. To supervise this generation, the image registration network then deforms the generated atlas to the two input subjects under anatomically meaningful guidance. This guidance is implemented by (1) minimizing the distance between corresponding cortical vertices of the two subjects in the age-specific atlas space and (2) maximizing the overlap between the warped atlas tissue probability maps (TPMs) and those of each subject. Compared with 4D atlases built by state-of-the-art methods, our atlases exhibit sharper and anatomically more meaningful patterns, allowing better alignment of brain anatomical structures.