Wallen, a taxi driver, said the footage showed his car being driven out of the lot and moved to another Park n' Fly lot where it was stored for the weekend before being driven back for him to collect it.
"One [driver] was thrashing it around there," he said. "What he was doing was thrashing it from basically a standing start to about 70km/h, then slowing down again."
He was "appalled" at the way the company's staff member had driven his car, he said.
"I can't understand how they can do that to a customer," Wallen said.
"The second guy [drove] it not like you should treat a vehicle, especially when it's not yours ... He was driving it roughly, not how you and I would treat our pride and joy - and that's what it is to me.
"I don't want anyone else to go through that."
Park n' Fly director Mohammed Alim confirmed the car was moved to another lot on Montgomerie Rd, as were all cars left with the company.
Montgomerie Rd was a 70km/h zone, Alim said, so the driver would have been just above speed limit although he would have broken company policy.
"I tell my staff, once they are on the road, no more than 50km/h. I'll have to have a word with this guy. He's only a part-timer," he said.
"I can understand. If it was my car I'd be like him. That's why I tell my staff not to drive it more than 50km/h.
"To me, customers' cars are important. Customers are important."
Alim said he and the driver would meet with Wallen last night so his staff member could apologise to him personally.
Wallen said he had been offered a refund since raising the issue with the company.
It's not the first time the company has come under fire for such incidents.
In November 2015 two Park n' Fly employees were disqualified from driving after being caught by police racing two customers' cars.
In another instance Neill Ellis, who left his car there while on a trip to Melbourne in 2014, posted a video on Facebook from his dash-cam showing the driver revving the engine, tooting, speeding through intersections and tailgating another car.