Generating simulation-ready tabletop scenes from task instructions is an intriguing and promising research direction in the field of Embodied AI. However, existing task-to-scene generation methods rely exclusively on large language models (LLMs) to predict scene layouts, inevitably yielding object collisions or floating due to LLMs' inherent limitations in 3D spatial reasoning. In this paper, we present STABLE, a semantics-physics dual-system tailored for simulation-ready tabletop scene generation. STABLE consists of two complementary modules: (i) a Semantic Reasoner, a fine-tuned LLM trained on a structured tabletop scene dataset to generate coarse layouts from input task instructions, and (ii) a Physics Corrector, a physics-aware flow-based denoising model that outputs pose updates to refine layouts, which ensures the physical plausibility of scenes while preserves semantic alignment with task instructions. STABLE adopts a progressive generation paradigm: by alternating between the Semantic Reasoner and Physics Corrector, it incrementally expands the scene from task-critical objects to background objects. Experiments demonstrate that STABLE successfully generates simulation-ready tabletop scenes that strictly conform to task instructions and significantly enhances the physical validity of scenes over prior art.