Great. I thought I'd look into this, and now I'm confused too.
Let me rephrase the issue.
The software shows the solar equator as seen from below between early December and early June, and from above the other half of the year. The maximum displacement angle corresponds to the ~7 deg axial tilt of the Sun w/r to the ecliptic. That this is correct is acknowledged e.g. here:
https://solar-center.stanford.edu/solar-images/latlong.html
This implies that the axis of rotation is tilted roughly in the direction to the vernal equinox, since about two weeks earlier in March the solar equator is maximally displaced upwards.
Now, sources (e.g.
https://link.springer.com/article/10.1007/s10569-007-9072-y) list the direction of the solar north pole in celestial coordinates as ~286 deg RA, ~64 deg dec. I.e. roughly in the opposite direction than the axial tilt of the Earth (w/r to the ecliptic). Which should make the equator visible from below from September to March (opposite to what
@Arbu wrote in the OP, I think).
So there's like ~60-90 (?) degrees/quarter of a year shift between what my reading of the coordinates suggests and what happens in reality. Where's the mistake?
I don't know about the OP, but myself, I suspect I might be misreading the coordinates. But I don't see in what way.