Three effects are seen here and it is hard to distinguish between them.
One is the presence and absence of fluorescent dyes. Sunlight has lots of UV and some tungsten lights emit UV light. In any event, this makes a print shift on the yellow - blue axis.
Second is the fact that some dyes shift to longer wavelengths or shorter wavelengths (bathochromic or hypsochromic shift are the technical terms). This may not take place in all dyes to the same extent and so the balance may appear to shift.
Third is the unit neutral of any image. Even silver is not 'neutral' but has a definite color cast to it that varies with how it is produced. A dye set had humps and bumps which your eye is 'tricked' into interpreting as being neutral in a perfect blend, but which is not pefect. So, you see one or another dye predominate as illuminant shifts.
This last item is involved with fluorescent lights which have a discontinuous spectrum consisting of peaks and bumps which may emphasize any imperfections in the dye set.
To describe it more fully, one would need to scan a neutral step wedge with a spectrophotometer using different illuminants and then the effects could be separated out and described more fully.
Sorry, but that was a very technical question you answered.
PE