This kit basically replaces the front valve 18495, spider valve 18502, and cable 18518 with a manual valve that installs in the heater hose between the water pump and the heater core. The new manual vale is controlled with the original dash lever marked LOW - TEMP - HIGH. Water comes from the top of the intake manifold and through the heater core and back to the suction side of the water pump.
Where the hoses go on the heater core is not a big deal. But flowing from bottom to the top may help expel air bubbles in the core. The reason for our directions saying put the manual valve in the "heater core to pump" hose is because that valve is directional - it may leak flow in one direction but seals flow in the other direction. See the arrow on the side opposite the cable bracket. Flipping it around to use in the other hose would put the cable bracket on the wrong side.