The chart is:
Number of partners
The flights must be operated by a unique partner, and only one flight per airline counts.
This promo is a tough one to hit a lot of miles on. US Airways does not count as a partner, so your first OneWorld flight results in 0 miles. The second only results in 500. So this is only worth it if you are planning to go big, and were going to fly multiple airlines anyway.
Still, it’s worth registering just in case. Sometimes I’ve accidentally earned bonuses I wasn’t expecting to earn.
Note: It appears that American Airlines DOES count as a separate airline, which is probably why the first partner earns 0.