It's common to intercept and reuse stock wiring with the manufacturer puts a molex plug at the door jamb. As noted above the factory tweeter and door woofer are on the same wiring (but in parallel, not series). Simply put, they get the same signal because the passive crossover is mounted to the tweeter. This is pretty typical across all makes/models that don't have fully active factory systems (typically reserved for higher trim levels).
Be sure to tape-off the unused harness and it's helpful to wrap it in something soft (like foam or felt) so it doesn't rattle around in the dash.
I highly recommend soldering if you're splicing into factory wiring. And in your case you're cutting the factory wiring since the harness is still connected to the factory radio. It's usually frowned upon to do this, which is why running new wiring is preferred. Instead of cutting wiring behind the dash/radio, you could intercept the factory door wiring in the kick panel where cutting is less likely to cause issues in the future (9[wire wouldn't be needed in this instance). Wiring behind head units is under a lot of stress when the factory radio is removed and reinstalled. Knowing what wire is what may require access to an online service manual so you can get the door molex plug diagram.
If you do cut behind the factory radio, be sure to insulate/tape/heatshrink each wire separately to prevent shorting out. The factory wire covering (usually fabric or plastic split loom) needs to be pulled back and you'll find the factory wiring is likely secured in several places to help alleviate strain. Just take your time and try to make it be as strong and secure as the factory wiring was.
Note that the other benefit of 9-wire is that you can use 4 conductors to give the signal to the amp (connect to head unit outputs) and 4 conductors to power the factory speakers (connect to the speaker side of the harness). The 9th wire is for remote turn-on, for which you'll look for 12V when the car is on.