If a person is under the Marchman Act, do they have to stay in a locked down program?

Typically, the court does not order somebody into a lockdown facility. The Marchman Act is a civil procedure, not a criminal procedure, where you could be incarcerated. However, that being said, if the court orders somebody into involuntary treatment to be assessed, to be stabilized, to be detoxed, and if the person then leaves the facility, the court can use its contempt power, which includes incarceration, as leverage to make sure the person says in treatment.