Head of player recruitment Iain Moody has been put on gardening leave and replaced with 23-year-old Kazakhstani Alisher Apsalyamov, who is a friend of Tan's son and has no football experience.
Despite reports of Mackay's fury, it has been claimed that the Scotsman has no intention of walking out of the Premier League outfit.
Chair of the Cardiff City Supporters' Trust Tim Hartley released a statement saying: "Fans will be concerned with the recent behind-the-scene developments at Cardiff City which appear to put into question the future of our manager, Malky Mackay. Supporters are surprised that who appears to have little hands-on experience has been put in charge of transfers at the football club.
"Fans want Malky Mackay, who has done a fantastic job as manager taking the club to the Premier League, to remain at Cardiff City. We don't want to see any action taken to undermine his position as manager and Cardiff City's efforts to have a successful first season in the top division.
"There are fears that the current developments could drive Malky into the arms of another Premier League club and that would be hugely damaging for the Bluebirds. Malky is a talented manager who has huge respect among the fans for what he has delivered. Fans deserve a clear statement on the position from the club on what has been happening and Malky's position needs to be made perfectly clear."
Cardiff are currently 14th in the league table after seven games.