This is the intended function of the game. Buildings in the construction process proceed on schedule, and are completed on schedule.
Any damage that occurs to the building during the construction process from combat, spies, or province capture is not “repaired” by the original construction order, as the budget of materials and time is specifically for the construction ordered at the start time.
Thus the building has been completed on time and on budget. Any damage that occurred during the construction process is now evident and will now need to be dealt with by repairing the building from the construction menu.
