My purely speculative guess is that each Battle will be, say, a dozen generic missions that have no requirements, but have a scaling difficulty. You can use any character, but they can only be used once and for that specific mission. The purpose of this is so even beginning players can do a couple missions and contribute. These common, generic missions will give credits, droids, ability mats, and other generic rewards.
Then you're going to have other missions that have much more specific requirements (maybe higher levels, higher stars, or specific characters and/or rosters) that give better rewards, commensurate with difficulty of the mission and strictness of the roster requirements. Like, shards, omegas, zetas, whatever.
All rewards get thrown into a pot, and when the Territory Battle is over everyone gets all the rewards.