We study the self-assembly of cylinder-forming diblock copolymers confined in ultrathin films by means of dissipative particle dynamics simulations paired with an elaborate polymer model that mimics the experimental reference system (PS-PHMA) as faithfully as computationally feasible. In particular, the effects of the polymer composition, film thickness, and surface interactions are investigated systematically, where we achieve quantitative agreement with experiments. We observe that the cylindrical domains change their orientation from perpendicular to parallel with respect to the substrate twice as the film thickness is increased. Furthermore, the onset thickness and the sharpness of this transition strongly depend on the microscopic details of the copolymers and their interaction with the substrate.