The diagram above is incorrect.
For the coil split to work, the linked red/white conductors need to be shunted to ground.
In the diagram above, the red/white pair is neither grounded for splitting nor does it become the sole output.
If red/white were intended to be the Split mode output, the black conductor should cease to be connected as an output.
You achieve the same if you swap the order of coils in that "train".
That is,
white & bare to ground.
black & green to the splitter switch
red to hot.
BUT then, you should ground the link (black & green).
This is a neater way than to shunt the slug coil to the hot path (as commonly done).