Update: Capitar seems to be a neutral faction. The other Humans fertilize the land (it becomes more greenish), the Fallen desecrate the land (it becomes more blackish), the Capitar neutralize the land (it removes any color change and removes any color change). So they pay only on greenish and blackish land (and swamps).
The Cities of the Capitar neutralize the swamps, the fertile lands around dragon statues, the desecrated lands around spider webs. If they conquer a city of another faction on the beginning of the next turn they immediatly switch the lands in their influence radius to neutral, removing fertility or desecration.