If you choose to keep supporting The Institute, you will be relayed to the Mss Fusion skyscraper roof. You can relay to the Mass Fusion and continue supporting this faction to leave the area and inform the Brotherhood to switch your loyalty. Fillmore wants you to retrieve the Beryllium Agitator from Mass Fusion. Speak with Allie Fillmore to start the quest.
Objective: Relay to Mass Fusion, search for Beryllium Agitator, reach the reactor level after getting the keycard, unlock the reactor and get the Beryllium Agitator, remove reactor level security and exit the Mass Fusion. Agree to keep supporting this faction and return to Father. You will have to visit the conference room in The Institute and debate with division heads. Objective: Be present for directorate meeting, talk to Father. Once you’re done, visit the CIT ruins to speak with Father. Find and deal with them as Father wishes. Some Synths have escaped the facility and ran away to Bunker Hill. Source: FALLOUT 4 The Synth issue and fear of the Institute are widespread in the Commonwealth, and several factions have their own ideas of how to deal. Speak with Father to trigger this quest for The Institute.