The tweeter wire is just split off of the same signal that the stock door woofer gets. If you look at the stock tweeter, you can see the capacitor on the back that serves as its passive crossover to filter out lower frequencies.
The woofer also receives a full range signal. All you should need to do is cut the stock woofer wires and feed them into the + and - terminals on your crossover. Then run wires from your crossover to your new woofer and tweeter.
The stock tweeter wires can be cut and capped off with either electrical tape (not recommended) or a end cap style crimp (recommended).
If you followed the same LOC/Amp/Sub install guides as are on the forums, you have no power being fed to your speakers directly from the HU, it is all coming from the amp.