A report from The Athletic's Shams Charania detailed an incident where McMillan had not approved Young's decision to skip a team shootaround to focus on treatment for his minor shoulder injury.
It is said to have resulted in an ultimatum, with McMillan telling Young he would have to come off the bench if he wanted to play against the Denver Nuggets on Friday, with the 24-year-old two-time All-Star instead deciding to not show up altogether.
The Hawks officially attributed Young's absence to his shoulder injury, before the report brought new information to light, prompting McMillan to call the whole fiasco a "miscommunication".
The report also included a line citing anonymous sources saying "it's the latest situation that has caused many people within the Hawks to question Young's leadership approach" – pointing to similar friction between Young and former head coach Lloyd Pierce as a main factor behind his departure.
In his first media appearance since the news broke, Young said he was frustrated it all became public.
"It's hard for people who don't know the full situation to understand it," he said on Monday. "Like I said, it's a private matter made public, which was unfortunate. If it stayed private it probably wouldn't have been as big of a deal.
"It's unfortunate. My job and my goal is to win a championship, and that's all I'm focused on.
"When you're an outside guy like [reporters] are, and you don't understand a private matter and private situation, you should probably stay on the outside.
"It's unfortunate that everybody has to understand and know a little bit of the details that went on inside. I mean, inside here we're all good.
"If you've got any more questions about that you can talk to somebody else about it. That's all I've got to say about it."
The Hawks ended up with an impressive win against the Nuggets, with rookie A.J. Griffin taking advantage of his opportunity in the starting line-up to score a career-high 24 points.