I click the Position stopwatch at the start position, keyfrane appears. I then drag the playhead, I move the object, no keyframe appears, and the position of the object has also changed at the start position.
PS 2017, same problem in 2016, no problem in CS6.
Win 7, 23 gb
Make sure you've selected the right keyframe. (Indicated by a yellow color.) I believe also that you need to use the "3D Meshes" option in the Timeline, not the plain-vanilla "Position" option to move your object around the 3D space.