Head inside Acadia and talk to the leader, DiMA. After the conversation with him, he’ll tell you that you can talk to Kasumi. At the same time, another quest will appear. (Acadian Ideals) You can talk to his co-founders, Chase and Faraday. Find Kasumi in the bottom floor and talk to her.
During the conversation with Kasumi, you’ll have the option to convince her that she’s a synth or not. Later on, she’ll tell you about something possibly deeper, a secret that involves DiMA and the whole island. If you agreed to help her with her investigation, you’ll have to choose whether you want to eavesdrop, hack Faraday’s terminal, or simply talk to DiMA. Those three methods will be this quest’s optional objectives.
Faraday’s terminal is Master-level so unless you have acquired the necessary perk to hack these level of terminal security, there’s no way for you to be able to do it using this approach. Faraday doesn't carry the password as well so pickpocketing it from him is not an option as well. You can also demand answers from DiMA by passing one of the two speech checks.
To gain access to the storage room, you have to pick the Expert-locked door. Once successfully, interact with the spot to hide and wait. All you need to do is to eavesdrop to their conversation.
Once done, you can talk to DiMa directly and tell him about what you’ve learned or pick up Faraday’s Program holotape on his table. He’ll then suggest for you to infiltrate the Children of Atom and pose as a recruit. If you’re already a member of the cult before this part of this quest, then it will be a lot easier. After learning the details, talk to Kasumi to complete the quest. The next quest will start afterward.