I think you have to make her a minor, at least in the US. The police have no cause to remove a legal adult from the home and won't. If she was seventeen and there was no plan for temporary custody in place (I can elaborate on that) child protective services would be called and she would be placed in emergency foster care. Given the foster care system she'd probably move multiple times in the first week and she could overhear what happened, if you want to play it that way. I'm not sure when they would tell her, but I have a friend who is a child advocate/lawyer, I can run it by her if you want.
A nineteen year old, in the US, would have no support services. She could stay in the home until the landlord kicked them out, the taxes or mortgage wasn't paid, and evicted. For a rental situation eviction can take up to a year, depending on the state. If it is a mortgage or taxes not being paid on a private home, it could take years. Either way the story would be on the news. If the real family showed up and offered her a home, she could go with them, because she was an adult, but it would be a hard sell to explain to her why she should without telling her what happened right then.
Sorry I know this wasn't exactly what you were looking for.
Edit: I thought about it some more. Your question is what would a psychologist do? Given that a psychologist is under a ethical, and possibly legal, obligation to act in the best interest of the patient, regardless of who is paying the bill, the psychologist would not withhold the truth about the situation for one minute, especially for a teenager. The situation is traumatic but there is no benefit to the patient and possibly additional harm to be caused, by waiting to tell them.