On Default Cube, select face, Inset it, Extrude it 'inside' the cube, add Bevel and Subdivision. This is the result.
I recently switched to the latest Blender version, and I could be wrong, but I don't remember the same behaviour in older version.
This is Default Cube, no extra vertices, no wrong face orientation.. And on Cylinder the process is working as expected. If I switch Subdivision to Simple, it looks as expected, but somewhat rough.