"We weren't happy right away. So, of course, it caught us off guard, but it was more the timing than anything else.
"It was last minute and it didn't give us much opportunity to discuss it with our sponsors and make sure that they knew what was going on."
Cycling New Zealand defended Villumsen's choice, stating nothing in UCI rules stipulated a rider had to use trade equipment at the world championships.
"The bike and equipment that Linda used was the overall package that CNZ believe was optimal for Linda's performance, especially regarding her position on the bike.
"Aerodynamics is one of the biggest factors in time trial performance."
Cheatley agreed, saying Villumsen had tested the Trek in wind-tunnel conditions and it was the best choice.
She could not get the front end of her position low enough on the UHC bike and the Trek was a smaller cycle which her team did not make.
"It proved that [decision was correct]. That bike was suited to her.
"At the end of the day, she got over the line by two seconds, which shows that she needed the right bike."
The New Zealander, who was frustrated at coming second or third at the time trial during the past five years, was within her rights to choose her own cycle as she was not representing her professional team.
"I presumed that was the case in her contract, and that was the case," said Cheatley.
"It happens all the time in Worlds and Olympics - you're representing your country."
Therefore, Villumsen painting the bike all black to match her national colours was not just patriotism, Cheatley said.
"That was a respect to her team owners, not exposing the [other] brand to the world.
"Even though everybody in cycling knew it was a Tech. From the people I saw talking about it on Facebook, [they] knew what it was.
"She was just subtly getting on with it. Her helmet was the same - all black. And that was for aerodynamics."
Tamayo acknowledged Villumsen had taken a calculated risk and banked on winning the title, which would make it harder for her team to fire her.
"Our sponsors are looking for a bit of an apology from Linda but we have as a team internal policies as far as fines for athletes as being not sponsor correct but we'll deal with that internally and not publicly.
"She could be fined within the team."