Is the association of fluorescent minerals calcite, fluorite, and apatite with fluorescent rare-Earth minerals a coincidence?
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.