The in-game clock runs at exactly the same speed as the real world. If the construction of a facility takes 15 minutes, it will be completed in exactly 15 minutes regardless of whether the game is exited or the mobile device is powered off. This allows players to compete against one another in a world where city and battle conditions can change by the minute.
Attacks made by other players will also progress in real time. This means that you may be susceptible to getting your castle attacked during late hours, early mornings, or during the routine maintenance (if the army is dispatched before it). Game mechanics like Entrenchment Mode (5 hour siege immunity) are available, but you will likely be forced to fend off the attacks or rely on your fellow alliance members.
Season lengths can last for several months. The timing of when the Season ends will be determined by the game operators. A system message is sent to all players beforehand. This will be a last call for players to make their final moves to determine the greatest victor for that Season.