Contrast-enhanced computed tomography (CECT) is pivotal for highlighting tissue perfusion and vascularity, yet its clinical ubiquity is impeded by the invasive nature of contrast agents and radiation risks. While virtual contrast enhancement (VCE) offers an alternative to synthesizing CECT from non-contrast CT (NCCT), existing methods struggle with anatomical heterogeneity and spatial misalignment, leading to inconsistent enhancement patterns and incorrect details. This paper introduces PHASOR, a volumetric diffusion framework for high-fidelity CT VCE. By treating CT volumes as coherent sequences, we leverage a video diffusion model to enhance structural coherence and volumetric accuracy. To ensure anatomy-phase consistent synthesis, we introduce two complementary modules. First, anatomy-routed mixture-of-experts (AR-MoE) anchors distinct enhancement patterns to anatomical semantics, with organ-specific memory to capture salient details. Second, intensity-phase aware representation alignment (IP-REPA) highlights intricate contrast signals while mitigating the impact of imperfect spatial alignment. Extensive experiments across three datasets demonstrate that PHASOR significantly outperforms state-of-the-art methods in both synthesis quality and enhancement accuracy.