There is a Ballard short story, Thirteen to Centaurus that has the major elements you describe (fake ship that's really a dome on earth, residents don't know it's fake but psychiatrist does, it's an experiment to determine psychological effects of space travel, psychiatrist enters/leaves as he pleases). Couple of differences between the synopsis and points in the question. The astronaut is a 16 year old Wunderkind named Abel and sounds more like he had conversations with the psychiatrist (because he was curious about things) than him being questioned by the psychiatrist. Also sounds like the 'truth' that was revealed in the end was a 'partial truth' and there was another layer. The whole truth is revealed at the end of the story but the synopsis doesn't make it clear if that was conveyed to Abel.
The story was also turned into an episode of Out of the Unknown, a BBC TV series that ran from 1965 to 1971.
If interested in reading the actual story, you can find PDFs on the web by Googling for 'PDF Ballard Complete Short Stories'.