The pivot point is located at the centre of the surrounding box, which in the case of the tetrahedron is off-centre of the mesh.
You can set the pivot point to anywhere you want it to be, as long as it is a vert, by right-clicking and selecting “Set pivot point”. So you would need to either cut in some edges to get a vert located at the centre, or you can make a facet, place it so that one of the verts is at the centre-point and set the pivot point to that.
Bit of a nuisance, but not that difficult to do:)
Be aware, though, that when you take the mesh into a rendering app, it will not respect the re-set pivot point and will set it to the centre of the bounding box. So, changing a pivot point is only useful during the modeling process and won’t be of any use further down the line in the animation process.