The unsteady reflection of detonation waves over cylindrical convex surfaces is numerically investigated using a high-resolution adaptive mesh refinement technique combined with a detailed reaction mechanism. Results reveal that cellular instabilities complicate the determination of the transition point from regular reflection to Mach reflection. However, the triple-point trajectories connecting the incident detonation wave and Mach stem remain largely unaffected by these instabilities. This consistency is confirmed by reducing the radius and the initial angle of the cylindrical surfaces. Finally, no universal scaling is observed across all configurations. At larger radii, the triple-point trajectories tend to stay closer to the surface.