Why at night do bright lights seem out of sync with everything else?

In the daytime, the light display is seen in context with everything else in the background. In the dark, your brain pays a disproportionate amount of attention to the display since it’s the brightest, most noticeable thing around, and it’s removed from the context of the background.

There’s a short time delay between light falling on your retina, the image persisting in the retina, and your brain processing the information. We normally don’t notice this time latency, but it becomes pronounced under conditions like you describe—moving a light in the dark. I’ve seen that effect many times.