How did people learn that Tommy was an alien in the movie The Man Who Fell To Earth?

In the film he gives himself away to Doctor Bryce inside the spaceship. He's evidently an accomplished scientist and inventor from England but who's never heard of the Latin language, which is basically unthinkable. Bryce later proves his thesis by taking an X-Ray photograph of our hero.

Bryce: Well, anyhow, Per ardua ad astra.

Tommy: [looks quizzical] I beg your pardon?

Bryce: That's Latin.

Tommy: [looks more quizzical] Latin?

Bryce: You must know that in England. Royal Air Force. Their motto

As to how the authorities know about him, in the source novel we see that government have had their suspicions about him for quite some time. His personal history is extremely odd (not to mention easily confirmed to be fake), and his persona as an eccentric billionaire inventor with an obsession with space travel has attracted considerable attention, leading to them surveilling him for years and searching his properties, noticing oddities such as a packet of aspirin with crude squiggles in place of writing. They finally decide to take him into custody and subject him to medical examination when they gain explicit confirmation from his own mouth.

Bowen still seemed amused—possibly with himself. “Not very likely,” he said. “As a matter of fact I might as well end all of this fencing.” He looked at Newton carefully. “One of the fascinating things about it is that a… a person of your intelligence could make so many blunders. Why do you suppose we happened to decide to pick you up when you were in Chicago? You’ve had two months to think about it.”

“I don’t know.” Newton said.

“That’s what I mean. Apparently you—Antheans, isn’t it?—aren’t altogether accustomed to thinking as we do. I believe any ordinary, human, detective magazine reader would have realized that we were bound to have had a microphone in your room in Chicago, when you were explaining yourself to Doctor Bryce.”