Is the association of fluorescent minerals calcite, fluorite, and apatite with fluorescent rare-Earth minerals a coincidence? If I understand this answer and this comment correctly, minerals like calcite, fluorite, and apatite are "commonly associated with (Rare Earth Element) REE deposits", and like some REEs also fluoresce when exposed to UV light. But the intrinsic fluorescent properties of those minerals are not caused by REEs.

Is this just a pleasant coincidence; the presence of one fluorescent mineral is often associated with the presence of another fluorescent mineral even though their fluorescence mechanisms are different?

Or do minerals like calcite, fluorite, and apatite tend to fluoresce because they contain REEs, thus observation of their fluorescence is a direct indicator of the presence of REEs? Or do REEs only modify the color of their fluorescence, but not necessarily cause it?
The answer to your question is probably the second:


  Or do REEs only modify the color of their fluorescence, but not necessarily cause it?


I will give an example of apatite. Here's a cathodoluminescence (luminescence excited by electrons) energy spectrum of a natural apatite. Source.



You can see several different rare earths triggering the luminescence, but there's also manganese. Apatites from granites usually have lots of manganese, and very little rare earths. So their luminescence would be dominated by the 2.1 eV range, which would be yellow. In contrast, apatite from REE deposits would be dominated by Ce, giving a blue-violet colour. They will also have lots of Nd, but that does not help us because it's in the infra-red range.