Djokovic had split up with Vajda, who had worked with him for much of his career, in spring but brought the Slovakian back into the fold a year later.
And the 53-year-old has revealed that on his return, he asked for Imaz to step back from Djokovic’s team.
“I was pushing his end, though it was not my No 1 condition,” Vajda told Slovakian outlet Sport.
Even before the 2017 split, Vajda himself had been moved into the wings by Boris Becker, who between 2013 and 2016 guided Djokovic to six Grand Slam titles and the world No 1 ranking.
After they broke up, the German claimed his charge had not been prepared to practise enough and when Vajda returned earlier this year, he appears to have asked for assurances regarding Djokovic’s commitment to tennis.
“[The first condition] was that I have to see Novak personally. The second was to set specific rules and plans in the coming months,” Vajda added.
“At the second joint tournament in Barcelona we had a complete team at our disposal, we sat and talked.
“We wanted other people around him not to intervene as much as it used to be before, we told him that we would not be pleased if it was again.
“We did not want to treat tennis as a philosophy but as a practice.
“He is primarily a tennis player and he must know what his priority.”
And Vajda was also keen for Djokovic, whom he felt had lost a level of physical conditioning, to bring back fitness coach Gebhard Gritsch.
“Novak is an excellent prototype athlete,” Vajda said.
“He has an athletic figure ideal for tennis with excellent muscle fibres.
“But it was necessary for the muscles to strengthen.
“Although its diet is mostly vegetarian, it also needed to get animal proteins.
“Without them, it is simply not possible. Therefore, he had to adjust the diet as well.
“It included more fish in it, as other meat he does not eat.
“He has been given the right nutrition and is now compact. His muscles are perfect and physically feel great.
“Right now he has the right habits and he does everything he needs to be a champion. Hopefully he will hold on to the US Open, too.”