Opening a fixed mini player automatically is a feature offered by the website and is created via JavaScript if the main player is scrolled out of view. A lot of websites now have a fixed (pop-up) mini player in one the corners once you start playing a video that stays visible if you scroll the page. This website mini player shouldn't be confused with the Firefox PiP (picture-in-picture) feature (you likely see the Firefox PiP icon if you hover the mini player).

You would need to use a content blocking extensions to hide such a player.