The diagram is correct.
Do you have a multimeter? If so, measure the resistance between the two outer lugs of the volume control. With the pickup still soldered in you should get a reading of about 8k when the volume control is turned up, an zero when it is turned down. If you get anything else than zero, there is your bleed - or lack thereof, since with the control to zero, the entire signal should be bled to ground.
If you get the zero reading, carefully check your connections. If you get a different reading, disconnect all wires to the volume control and measure again. Still no zero when turned down - the volume pot is bad, replace it.
The tone control should continue to work when splitting the coils. Since the pickups do have a higher resonant peak as single coils the tone control will work in a different range. If it does not work at all, there is a wiring error. Check and double check your connections.
Good luck,
Stephan