Most of the time, when you shoot HDR photos, you’ll be taking multiple exposures. So, you often end up with the old “ghosting” problem in which an object changes its XY across the plane.
I contend that you don’t have to worry about that if you want to give the impression of time flowing. This bleeds into my discussion yesterday about impressionist feelings within photos. Yes, photography is about stopping time, normally, but it doesn’t have to be.
If you are taking an HDR of a moving river or flowing steam (like below), then I like to allow the ghosting to remain. It gives a feeling of movement and time, and that’s a nice thing to communicate in a photo.