This is, of course, impossible. There was an illustration, showing that this is impossible. But no proof that it had ever actually happened. The poster just took it as read. So I decided to find out where the story came from.
A little searching brought me to the only place I can find where anyone claims that Polaris has ever been seen from Reunion Island: a massive book called The Greatest Lie On Earth: Proof That Our World Is Not a Moving Globe by Edward Hendrie. There is no other source for this claim, even on flat-Earth websites.
Fortunately, Google books has a preview inside where I found page 105, where Hendrie says:
Below is a time lapse photograph of the North Star (Polaris). The photograph was taken in October, 2008, from the Le Make Reunion Astronomical Observatory on Reunion Island.100 That observatory is at an altitude of 4,921 feet and is located at 55.39° east longitude and 21.5° south latitude. The photograph was taken by Laurent Foumet and lean-Philippe Olive, who are members of the Club Astro Astrium in Toulouse, France. Olive and Foumet used an Olympus camera, 28mm f/8 lens, 2 hours and 40 minutes exposure time; Ektachrome 210 ASA film.Note how detailed this is, how it looks so accurate and well thought-out. It even has a source reference. Very convincing. Except for two things: the photograph, which I will give you the link to presently, which shows, in the center of the star trails, not a bright star, but a dim cluster; and second, that I know what is described is impossible.
So, let's check out that reference. Hmm. Seems that this picture is not of Polaris at all. It says right in the text that these are southern circumpolar stars.
So, is Hendrie just missing something? Or was he just counting on everyone who read the text not bothering to check the reference? In either case, it seems that anyone who writes a 400-page book claiming that the Earth is not a globe should have a better standard of evidence.