This is due to the response time of your monitor. Overdrive is something that usually controls this, if you have it. It's also sometimes called Motion Blur Reduction. It's the simple response time. You may see this advertised on high-end gaming monitors, like "1ms response time!". That's all this is about. So, what you're seeing is a slow response time, but that's to be expected from a notebooks display panel. It's not meant for high-performance gaming with very little motion blur.

So, I'm afraid that you can't do anything about it. I have NEVER heard of this being controlled with software, like through the driver. I doubt that's even possible.

The reason you see it more when f.lux warms up the color temperature is just due to the color. It's always there, whether you can see it or not.