The high penetration of renewable energy increases grid volatility, necessitating flexible demand-side resources such as District Cooling Systems (DCS) with thermal storage. However, the multi-timescale coupling of equipment, pipelines, and buildings makes it difficult to integrate high-fidelity physical models with optimization. This paper proposes an FMI-based co-simulation framework for day-ahead DCS optimization. A fullchain Modelica model is exported as an FMI 2.0 CoSimulation FMU and coupled with MATLAB optimizers. The main contribution is a standardized FMU-in-the-loop workflow for day-ahead mixed-integer nonlinear programming (MINLP) scheduling with discrete unit commitment, together with a systematic quantification of the accuracy-runtime trade-off induced by FMI communication settings. Sensitivity analysis identifies a practical configuration for the investigated case, while a comparison of the genetic algorithm (GA) and surrogateopt reveals the solution-quality and computation-time trade-off. Compared with storagepriority control, the cost-optimization scenario reduces operating costs by 0.97%, the energy-optimization scenario reduces electricity consumption by 4.58%, and the carbon-optimization scenario reduces CO2 emissions by 4.20%. The physical feasibility of the generated schedules is verified by dynamic FMU simulation.