few things must be clarified:
1) What are theta and phi and how they related to E-plane and H-plane.
there is a nice image in this topic:
https://www.edaboard.com/threads/242762/
From this image:
H-plane, angle is phi, it is horizontal plane
E-plane, angle is theta, it is vertical plane
Come back to your image:
broken link removed
If CST use similar angle names for E/H plane, then
Theta horizontal -> E-plane is horizontal
Phi vertical -> H-plane is vertical
So it looks reversed to me.
On the first image E-plane is vertical, and on your image it looks like E-plane is considered horizontal
2)We must know where E-plane and H-plane must be on your antenna
as on volker@muehlhaus for patch-images:
E-field and H-field vectors:
if feeding port is on the right, then E-plane is horizontal. But usually feeding port is considered vertical (at the bottom), then E-plane would be vertical.
So i think we are pretty near to understand how swapping is occurred. The only thing left is to clarify how your antenna looks like (it is not clear from image), to understand where real E-plane is, and is it in horizontal position. If your antenna's E-plane is vertical, then result probably swapped, because in 3D view E-plane considered horizontal.
Problem arises from the fact that CAD software does not automatically determine antenna polarization (i guess so).
p.s. in volker@muehlhaus patch images there are E-field and H-field vectors. Probably CST can do it. But it is also can be deducted from knowledge on your antenna configuration.