Darkside left (from the pole) to darkside bottom (at the equator) implies a 90 degree anticlockwise rotation, doesn't it?

However, my toy model was only intended to demonstrate the general principle that the tilted terminator is to be expected when viewing from midlatitudes.
To the toy model you have to add the fact that in the real world the moon may have a more northerly or southerly declination than the sun, depending on the season and the moon's orbital tilt. (Whereas in my model the declination of moon and sun are always equal and zero.)
So in the real world, even when observed from the pole, there may be a pre-existing tilt to the terminator, which would then interact with the effect I've described as you moved south.

Does that help?

Grant Hutchison