I just finished watching a video that explained some of how UV light looks with a UV camera. In the video, at one point the UV camera made everything distinctly green. At another point, everything was purple instead of green. The video had demonstrations about absorbing UV light and how that made things darker vs. reflecting UV light made them brighter, but I still don't know how the green to purple shift happened.
Was that an issue of the camera lens? Is my own color perception somehow incorrect and there was never any green at all?
Here is another video about a UV camera from Veritaseum. The World in UV. It does not explain what you asked, but it does make something clear. The UV camera detects UV light. It then shows it to you with light you can see. That light is visible. So you can conclude that a UV camera is a UV to visible converter.
To a degree, that is all you need to know. You can't see UV, so the camera has to pick some color you can see. It doesn't really matter which one it picks. I depends on the manufacturer.