Computing the actual intersection of a picking ray and the geometry of a tileset is not entirely trivial. Keep in mind that 3D Tiles has a built-in concept of “Level Of Detail”: You might see a coarse, low-resolution geometry when you’re far away. And when you zoom in, then the finer, more detailed and high-resolution geometry is loaded. Additionally, there may be multiple tilesets and geometries that are overlapping - so there will be multiple intersections with the ray.
If you describe your goal in more detail, then maybe someone can provide some hints about how it could be accomplished.
In the meantime, maybe you want to have a look at the examples in the Picking Examples Cesium Sandcastle (maybe ‘Pick Position’ or ‘Drill-Down Picking’), to see whether one of these examples is similar to what you want to do.