Hm, here are a couple of things to consider. The different bases have different coloring so that can affect the way the color shows. "Supposedly" each base has a different formula to correct for this but my own experience doesn't bare that out. The sample pots for BM are kind of warm and the advance is fairly white. In my experience I recall it as being warm too but also very bright white. When I was shopping I ended up getting quarts in the formulas of the paint I was considering. I ended up spending a small fortune in regular samples and then quarts of the different paints. In my own experience I had a custom color made in cabinet coat (also a BM product) and wanted the same color in aura and what was a golden white in CC was a pinkish grayish white in aura. In multiple attempts to correct it the shade never matched up so I went with something else.
As for it matching the primer you could either be seeing the primer through the paint or it might be a really close match. When my custom gallon of aura didn't work after three corrections I ended up "painting" my room in primer because it was such a close match for my custom paint!!