Can you post a 1:1 crop of the marked areas or the full file? I'm intrigued that the first case you identified shows a fainter star in place whereas in the second I found, there's no star visible in the first image, at least in the posted picture.
If the stars get spuriously brighter, there may be a problem with the sensor (say, a spurious amplification of existing data - and to be clear, this is pure speculation on my part, trying to identify possible causes).
If the "new star" also appears where there was no real signal at all (no star), then the problem is not with amplification but rather with the sensor cell itself. By the way, what camera did you use?
Finally, can you blink images from previous sessions? You may find more cases and if you register the images, it'd be easier.