I'm pretty sure it's not always like that, though. In pictures 4 and 5 the ship is in various stages of tacking. What you're seeing isn't sail 'twist,' it's the yards being braced around consecutively instead of simultaneously. When you are tacking the yards are swung around by the wind as much as the hands at the braces. Each yard was trimmed a bit differently to begin with, and the wind is fairer aloft, so the various sails will come aback or start drawing at different times. Or if you are off with your timing, traversing the lower yards might be a long slow slog against the pressure of the wind.
In other situations where you are trimming the yards, there's no reason a well-drilled crew wouldn't do everything simultaneously.