Can you post a pic of these pig tails that you have? Or at least describe them? Is one side a connector that plugs in to the ballast and the other side just red and black wires? If so, then you need to either cut off your factory low beam connectors and splice the pigtails on to them, or you need to buy a pigtail with an H1 male end and splice the HID pigtail to that to create a plug n' play converter. Doing the latter would be best if you'd rather not cut in to your factory harness.
If I were doing this, I would use a relay system though. HID setups need strong, consistent power to function correctly. Running them through the factory wiring designed for halogen bulbs isn't an ideal solution. With a relay setup, the HIDs will be powered by a direct connection to the battery and the factory low beam wiring becomes simply a trigger to turn the headlights on instead of also being the power source. This is how aftermarket HID setups work.
EDIT: One other consideration here...the beam on the JDM headlights points slightly to the left (because right-hand-drive) instead of to the right like on USDM cars, so be prepared to get flashed by annoyed drivers on a semi-regular basis. I've never done the JDM headlights personally, so I don't know if there's some way to manipulate the shield or to pull it out and replace with the shield from the factory headlights. Maybe someone else can chime in on that.