Vision-language-action models (VLAs) are promising general-purpose robot policies, but adapting them to new tasks typically requires costly task-specific teleoperation data. As an alternative, we study one-shot demo-conditioned VLAs, where a robot policy is conditioned on a single demonstration video of an unseen task. We find that existing end-to-end approaches often struggle when successful execution requires precisely localizing small target regions. To address this limitation, we propose SeeTraceAct, a demo-conditioned VLA framework that encourages precise spatial grounding through visibility-aware prediction of future end-effector traces. To enable reproducible evaluation with cross-embodiment demonstrations, we introduce and release RoboCasa-DC, a demo-conditioned extension of RoboCasa with episode-paired humanoid videos. Experiments on RoboCasa-DC and a real-world benchmark, where a Franka Panda arm is conditioned on human demonstrations, show that SeeTraceAct outperforms baselines, achieving the best success rate across all four RoboCasa-DC settings and improving real-world average success by 12.5 percentage points.