"Nick - last point was really borderline."
Kyrgios threw a mini temper tantrum in response, telling Dumusois: "I don't care, bro".
The two continued to discuss at the following change of ends as the Australian questioned whether the umpire meant borderline good or bad.
"We don't really know and I don't think he really knows exactly what his potential is".
"Nick plays his best tennis when he's fresh, when he's enjoying himself and he's engaged", said Woodbridge, according to the Melbourne Age.
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He later sarcastically asked Dumusois "was that borderline?" after serving an ace.
The 23-year-old rattled off another three aces to close out the game, pointing at the official each time.
"I think we're two very different characters", said Kyrgios following his loss to the Swiss at the US Open. "But when they get aced ... it's fine right, they walk side to side, it's fine", Kyrgios ranted to his box.
He later cautioned the umpire: "You know I literally could just go to the ATP office after this and say I just felt put down from your comment and you'd be in trouble, right?"
The Shanghai Masters has been a particularly unhappy hunting ground for Kyrgios over the years, with this being the fourth year in a row that he has stoked controversy at the competition.
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At last year's tournament, Kyrgios smashed two balls out of court in frustration and stormed off midway through his match with Steve Johnson in the first round.
Todd Woodbridge believes Nick Kyrgios is copping extra scrutiny from umpires but doesn't help himself by the way he engages with them.
And in 2015, he was fined USD1,500 for using obscenities during a match and calling the event a "circus".
Now ranked 38, it will take a major turnaround for Kyrgios to pick up a seeding for next year's Australian Open.
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Kyrgios made no initial public comment after his defeat by qualifier Klahn, but has previously spoken of his intent to learn from Federer.