Chelsea visit Southampton in the Premier League on Saturday having experienced defeat only once since Hiddink's arrival in December after a traumatic opening half to the season which led to Mourinho's sacking and in which he frequently criticised his players.
Koeman's team has similarly improved after a poor run, and the Dutchman, who is familiar with Hiddink's methods having been coached by him at PSV Eindhoven, revealed he expected that would be the impact he would have.
"He is always defending his players and that was good for Chelsea at that moment," said Koeman, 52.
"He was the right man at the right moment and the players are looking more comfortable and he has given them confidence.
"I was expecting that because they have good players with good qualities
The way the manager is dealing with the team is good for this moment.
"Why and when they changed the manager they signed Guus Hiddink for his second spell at Chelsea and he had, in the past, had a good relationship with the players.
"He is a coach with a lot of experience at all levels and knows a lot
He has a knowledge about characters of players and how to give them that important support to the key players."
One individual who has particularly thrived since Hiddink's appointment, on an interim basis, is Diego Costa, who had struggled from August to December under Mourinho despite contributing significantly to them previously winning the league.
Southampton have not conceded during their past six games, since the return to fitness of England goalkeeper Fraser Forster, but Koeman remains wary of the rejuvenated striker's threat.
"Costa is one of the best strikers because he is always on the move and making it difficult for defenders," he said.
"There is an emotional part in his character that makes it more difficult for himself but as a defender you need to be full of attention for 90 minutes because if you are not he will punish you.
"Everybody puts a little bit more attention about the return of Fraser Forster and him coming back has given everyone a boost.
"But the whole team is working hard to keep clean sheets and it is difficult to score against us because we have good organisation."
Source : PA
Source: PA