Friction-shift (rear) always changing up the gears
Rode downtube friction shifters bikes for a while. 
I can see two possible causes : either the shifter was too lubricated, or the screw isn't tightened enough. Try to tighten it more, but pay attention not to tear the screw. 
Usually the lever is pretty rigid when moving. If it's easy to move it to the point it moves alone, it's probably because it wasn't tightened properly.
If this does not work, you'll have to unmount it and delubricate the parts a bit.