Actually I suspect something more like this is happening: your local copy is running the simulation, while it's also being run on the server. Running it locally means you get no lag at all and running it on the server prevents cheating. The two simulations sync from time to time.
Preventing cheating might make sense in competitive PvP games, but makes no sense at all in a single player game that has traditionally been played offline.
*When I quit the game and came back the next day, my city was gone.