"MTV and Miley knew exactly what they were doing," a source close to Cyrus tells PEOPLE
Credit: Jeff Kravitz/FilmMagic

It was the twerk seen ’round the world – and it was all Miley’s idea.

Cyrus, 20, had been working on the VMAs performance of her hit “We Can’t Stop” – along with her racy duet with Robin Thicke – for about a month before MTV’s big awards show on Sunday.

“Most it came from Miley’s brain,” Cyrus’s manager Larry Rudolph tells PEOPLE. “But she collaborated with [her music video director] Diane Martel, who helped her conceive it and bring in the spirit of the VMAs. And with Todd James who designed all of those amazing bears.”

Though her skimpy, flesh-colored outfit, her suggestive use of a foam finger and close contact with Thicke, 36, were panned on social media, not everyone is criticizing Cyrus’s jaw-dropping performance.

Stars like Justin Timberlake came to her defense, telling one radio station, “Let her do her thing.” But the Parents Television Council issued a statement condemning MTV for airing the number.

So what does Cyrus, whose new record will be released Oct 8., think about the world’s reaction? “She couldn’t have been happier about the performance,” says Rudolph.

“MTV and Miley knew exactly what they were doing,” adds a source close to Cyrus, whose team wasn’t alarmed by the performance. “No one is freaking out.”

In fact, “We were all cheering from the side of the stage,” Rudolph says of Cyrus’s inner circle, which included her mom Tish. “It could not have gone better. The fans all got it. The rest eventually will.”

For more on Miley Cyrus’s transformation over the years, pick up the new issue of PEOPLE magazine, on stands this Friday.