The Rogue Summoners are a group of summoners which Midou, Tenma, and Tenjin are a part of. They banded together and entered the city of Kazamatsuri in order to search for the Key. Though is is unclear of what they intend to do with it.
Several years prior to the current story, Midou and Tenjin, along with Jasmine and several other children were used by members of Gaia in order to control a familiar called a Djinn and guard a top secret facility that grows crops used to create familiars.
Serving as pawns of Gaia for some time, the facility was attacked and they somehow made it out alive. It is mentioned in the route that they were saved by Tenma and his familiar, Krivoy Rog. After being saved, they formed the random summoners and ventured to Kazamatsuri in order to search for the Key for unknown purposes.
Midou, Tenjin, and Jasmine are saved by Kotarou and Luis from being Gaia's pawns and escape the facility due to Luis sacrificing his life in order to shoot down three 'scorched earth missiles'. They are taken to a shelter and placed in Jasmine's care. Eventually they create a haven that takes in both summoners and superhumans. Along the way they seemingly met Tenma.