Recent advances in Medical Large Language Models have shown strong performance in medical question answering and clinical knowledge understanding, yet real-world clinical practice requires long-horizon, dynamic treatment decision-making rather than static prediction. Existing medical agent environments are mostly turn-based, assuming patient states change after actions while overlooking natural disease progression and delayed treatment effects. We propose MedACE, a time-aware asynchronous clinical world model, where patient evolution is formulated as an elapsed-time-conditioned process driven by historical observations, treatment actions, clinical context, and disease-level knowledge. Built from timestamped MIMIC-IV trajectories, our JEPA-style simulator, MedWorld-JEPA, learns future patient state representations in latent space rather than directly generating noisy clinical observations. Based on this simulator, we construct an asynchronous treatment environment with global time advancement, closed-loop patient simulation, multi-step physician-agent interaction, and outcome-grounded rewards. Experiments on Hospital and ICU scenarios demonstrate competitive physiological forecasting, strong clinical consistency, and the importance of jointly modeling time, disease progression, and treatment effects. Agent evaluations further show that current LLM-based physicians struggle with long-horizon treatment decisions, highlighting our environment as a challenging foundation for future medical treatment agents.