I did some calibration and came finally determined why I was very confused. Please let me know if this is true for anyone else:
The quantizer seems to be an active process, despite the implications of the menu. Meaning: Map the pads per normal, then shift to a mapping that doesn’t include one of the mapped notes.
As a simple example, map ae(olian) C. Change the second pad to C# from D. C# outputs C. In the quantizer menu, cycle to io(nian). C# now outputs C#. No confirmation is necessary. Whatever you leave the quantizer on is what all pads are forced to, whether or not you map the scale.
This was super unintuitive to me! 
I couldn’t figure out why notes were wrong when I manually changed them. It feels like almost like a bug to me.
I guess the spirit is if you had a sequence running you could change it? But there’s no confirmation click, so the scale would warp as you cycle through the options, as it’s an “active process” rather than a straight voltage memory. I presume changing the key is the same deal, you can remap, but otherwise it just awkwardly tried to remap the notes to the correct key?
Herm. Anyone else have feels on this?
I feel like one of the key points of confusion for me is that pads are referenced by their note name assignments. So even if you change the key or quantizer mode, the “label” is still whatever it was when you mapped it. When it’s quantized differently, the “label” for pad 1 is C, the label for pad 2 is C#. And so on. The quantize mode and the key mappings warp all of those values around. There is no “unquantized” output, so this distinction is peculiar…
…and I guess I’m still wrapping my head around it.