These tractors use what is known as an "open center system". The oil flows from the pump to the PTO valve, to the Travel/Lift valve, to the oil cooler and back to the reservoir, ready for another trip through the pump. The lever on the PTO simply diverts 100 percent of the oil flow to whatever attachment is connected to the valve.
Either way, all of the oil flow ends up leaving the PTO valve and going to the Travel/Lift valve where a portion can be used to raise or lower attachments and either all of the flow can be sent to the drive motor or just a portion.
The oil is in constant circulation, ready to go to work for you at the flick of a control lever.
When you first connect up that tiller, remove one quick coupler on the tiller and stick the hose into a bucket. Then with the engine idling, open the PTO valve and flush out the tiller motor and lines. For the cost of a quart of oil, it isn't worth risking contamination to your system.
While the tiller will rotate in both directions, the tines are only sharpened on one side. If you are tilling hard ground, then the rotation direction is going to matter.
Even the PTO kit should be flushed out prior to installation for the same reason. The lines or hoses can be cleansed with solvent or with fresh diesel fuel. There is so little oil in the valve itself, it isn't worth bothering with if the ports look clean inside.