Accurate reconstruction of digital surface models (DSMs) from multi-date high-resolution urban satellite imagery supports large-scale Earth observation and three-dimensional city modeling, with 3D Gaussian Splatting (3DGS) emerging as an efficient solution. Existing shadow-aware methods provide shadow-related spatial evidence, whereas geometric priors are generally applied across the image or scene without using this evidence to allocate supervision. Consequently, regions where shadows overlap abrupt elevation transitions may remain geometrically under-constrained, producing spatially non-uniform elevation errors whose severity varies with the geometry covered by shadow. To address this issue, we propose Shadow-Adaptive Geometric Supervision for Earth Observation Gaussian Splatting (SAGE). SAGE is primarily designed for urban scenes dominated by regular human-made structures and retains image-wide altitude guidance while allocating additional geometric supervision at two levels. At the spatial level, patch-level shadow weights determine where a shadow-targeted local altitude prior is applied to constrain relative altitude agreement. At the scene level, SAGE computes the reconstruction-derived Shadow Geometric Complexity (SGC) from multi-view shadow evidence and gradient statistics of the predicted DSM. SGC is used as a scene-level descriptor of shadow–gradient contrast and determines how strongly the local altitude prior and the complementary Manhattan orientation regularization are applied. Experiments on seven predominantly urban scenes from the DFC2019 and IARPA 2016 benchmarks show that SAGE achieves the best mean DSM accuracy on both benchmarks while retaining minute-level processing.