She said the man was apprehended by police after only making it 50 metres from the hotel.
"They didn't even make 50 metres. Security and the police were on to it and it really does show the work of having the police on site.
"They could be immediately brought back into the facility. This is an example of the systems working as they should.
Air Commodore Darryn Webb said the 32-year-old man attempted to follow a staff member out of the gate, claiming he was a worker.
Webb said the man refused to show identification to staff who challenged him and then escaped onto Albert Street.
Defence Force staff followed the man until a police officer wearing a mask and gloves arrested him 100 metres from the hotel.
The man arrived from Brisbane yesterday, on 29 July, and has not yet been tested for Covid-19.
He will appear in court at a later date.