Mr Joga said he heard about "four or five bangs" before seeing flames shooting out from the engine. "I could see an orange light coming from the windows," he said.
Newlywed Malissa Siaea, making her way to Thailand with her husband, said the plane was "making funny noises when we were getting ready for takeoff".
"About 20 minutes into the flight fire sparked out of the right-side engine," she told Fairfax Media. "Then the plane swooped a little bit and started shaking badly."
She said a number of passengers didn't even know there was a problem until a man yelled out: "What the heck is happening?"
Another passenger, Calvin Boon, posted a video of the plane after it landed safely at Brisbane Airport. He thanked the AirAsia X flight captain and crew for their handling of the incident.
The budget airline blamed a "suspected bird strike" for its latest drama.
"AirAsia X Flight D7 207 bound for Kuala Lumpur, Malaysia was diverted after experiencing a suspected bird strike to its starboard engine," the embattled airline said in a statement. "Two bird remains were found on the runway."
AirAsia X CEO Benyamin Ismail said all passengers would be flown to Kuala Lumpur as soon as possible.
"We are following all regulatory guidelines to ensure the safety and wellbeing of our guests," he said in the statement.
"We would like to commend our pilot and crew members for their professionalism and swift action to reassure passengers who were on board flight D7 207 and to land the aircraft safely in Brisbane airport."
It comes less than a week after the pilot of a stricken AirAsia X plane told passengers to "say a prayer" after an engine issue forced the A330 to return to Perth.
Passengers on Flight D7237, en route to Kuala Lumpur, told how they heard a bang and looked out the window to see the left engine vibrating violently under the wing.
The aircraft started shuddering and a strong engine smell wafted through the cabin for a couple of minutes before the pilot went back to Perth Airport.
With terrified passengers in the "brace position", the aircraft landed safely at 10am, three hours after it had initially departed on June 25.
The incident is being investigated.