Why does my shower diverter allow water to flow to the tub spout?
Sure sounds like the diverter needs fixing or replacement. 

When the diverter is closed (sending water to the showerhead), it has to handle the full supply pressure.  When only closed two thirds, it sees significantly less pressure. Sounds like the force of the water, is pushing the diverter open. This allows water to flow out the tub spout, rather than being sent to the showerhead.

Depending on the make and model, you might be able to make adjustments, replace parts, or a full replacement may be required.