Amorphous oxide semiconductors have grown in technological relevance in displays, information technology, energy, and catalysis. Recent research efforts have converged on the need to develop design principles for the electronic structure of these materials. Here, we systematically vary the cation composition and annealing temperatures of zinc tin oxide films using atomic layer deposition (ALD) and study their process-structure relationships with synchrotron X-ray absorption near-edge spectroscopy (XANES). Measurements of the O K-edge, Sn M-edge, and Zn L-edge are analyzed with ab initio and nonlinear statistical modeling to understand the changes in geometric and electronic structure of the films. A key finding from this approach is the ability to measure the changes in the relative contribution of the Zn and Sn s orbitals to the density of states near the conduction band minimum. Furthermore, we identify and delineate critical process-structure design principles when working with amorphous oxide semiconductor (AOS) material systems: (1) use of complementary diffraction and absorption spectroscopy techniques to characterize the as-deposited coordination environment; (2) accounting for gradual and abrupt changes in coordination environment as a function of processing parameters (stoichiometry, annealing, etc.); (3) revealing and exploiting the relevant knowledge and interdependence of coordination environments, orbital hybridizations, the density of states, and band structures. In the future, this multimodal X-ray analysis and modeling framework can be applied to understand the process-structure relationships needed to optimize AOS performance in devices.