Hey @Thomas_Adolphi,
You say this works when the polygon is horizontal - can you post an image of what it’s supposed to look like?
This issue reminds me of this forum post. I think the answer might be the same - that you need to specify UV coordinates in your polygon for Cesium to know exactly how you want your texture applied (see my comment on that post and the sandcastle I linked).
Give that a try and let us know if it works or not!
Best,
Matt