Cesium OSM buildings floating in the air; could we set a custom ellipsoid, locally more accurate?

I just discovered the way to include OSM building data in a Cesium project. It sounds great but I also (re)-discovered my local ellipsoid vertical offset with the global WGS84 one (see pictures).

The "flying buildings syndrome" (they are certainly at the ground level referenced on the WGS84, but the local terrain tiles seem not, or I missed something).

We live ‘on’ the Bessel ellipsoid which is 50m lower than the WGS84.

I may be wrong in my hypothesis, so let me know if it’s the case.

Here is my question;

Did I miss something, e.g. to base the terrain tiles on the WGS84 ellipsoid?
If not, is there a way to fix this, for example by setting a different ellipsoid, more accurate locally than the global WGS84?
Or, any mean to bring the building back down to the ground?