Wondering about what tsukishima is after even more. Decided to reread chapters from "The Burnout Inferno". Back when Aizen started spewing BS like crazy.
Lets review the facts:
1. The fullbringers goal is to pass their powers onto a Substitute Shinigami, and become normal humans.
2. Tsukishima was apart of Ginjo's group(possibly the leader?).
3. After finding a Sub Shinigami and the others passed their powers onto them, Tsukishima killed the Sub Shinigami and the others who had passed their powers already, and vanished.
Honestly, I totally wouldn't be surprised if this whole arc was a dream or something.