I used to think the same thing -- that alk and CA don't really matter for anemones because they don't use them to build their skeleton/structure. However, alk can be an indicator of water quality. When alk is off or fluctuates a lot, it indirectly throws off other parameters: can cause swings in pH, an increase in nuisance algae, decrease in trace elements, etc.
Once I started to provide a more stable environment for my anemones, I saw a lot of the seemingly unexplained issues I used to see go away: random deflations, adjustment of zoox via expulsion (which is what we could be seeing with the OP's anemone), and changes in the anemone's size (typically slowly shrinking). And, in ways I can't explain, what I thought was allelopathy had been minimized, though it could be me adding carbon as part of my goal of providing that environment closer to natural sea water.
As long as your alk is consistent at 12-13 and your anemone's are used to it, they should be fine. My point was that they actually do care about alk, though most of it admittedly in an indirect relationship.