Earlier, AFP quoted one of the passengers as saying the plane was "shaking like a washing machine". Twin-engine aircraft like the A330 are created to fly and land safely with only one engine operating.
"He delivered us home safely which is awesome, everybody burst into applause when we landed", she said.
Some passengers posted videos on social media.
The airline suffered its first fatal incident in December 2014, when AirAsia Flight QZ8501 crashed in stormy weather off Indonesia with 162 people on board.
AirAsia is investigating the incident, but says there is no indication it was an engine issue.
Mr Parry said the most frightening time was the minutes the passengers were in the brace position as the plane came in to land, as they could not see what was happening.
AirAsia said in a statement that the flight had been forced to turn back due to a "technical reason".
"I feel fine but a lot of people I've spoken with are really shaken and quite apprehensive about the flight", Stevens said. "The plane erupted with applause once we landed".
"Our survival depends on you co-operating, and hopefully everything will turn out for the best", the pilot nervously told them.
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