1. The first person to pay tribute is Suzaku, because Suzaku's recovery and blood-sucking are the most obvious in the early stage.
2. After maxing out Suzaku's favor, give the tribute to Xuanwu, because Xuanwu also restores blood, although not as powerful as Suzaku.
3. After you have filled up the Suzaku Xuanwu, you can give it to Pangu, and Pangu will increase the chance of getting fragments.
4. After that, everyone can give tributes at will, but don’t give them indiscriminately. Giving at will means giving whatever you want.