It follows reports relations between the two camps have deteriorated dramatically after the fiery First Test, which also featured Nathan Lyon being fined 15 per cent of his match fee and hit with one demerit point after being charged with conduct contrary to the spirit of cricket for his reaction to the second innings run out of AB de Villiers.
Warner's stunning rampage in Durban was reportedly sparked by an alleged comment from de Kock about the Aussie opener's wife Candice.
Candice Warner is currently in Durban with the team.
A claim later emerged on Monday night that de Kock's personal slur directed at Warner was in response to Warner first crossing the line with a series of personal attacks directed at the South African keeper as he was trying to save the game with his bat in the second innings.
Proteas team manager Mohammed Moosajee suggested Warner got personal in his sledging and "whatever happens out on the field, you giving something you've got to take it".
The Proteas are privately alleging that Warner referenced de Kock's sister and mother in some verbals.
Separate reports claim the South African camp also briefed local media that Warner called de Kock a "bush pig".
A further report from South Africa's Independent Media — the first news site to publish the leaked CCTV footage from Durban — claims Warner "led an hour long attack on the field" as de Kock and opener Aiden Markram frustrated the Aussie attack on their way to eventually winning the series opener on day five.
South African legend Graeme Smith also said Warner "crossed many personal boundaries".
Aussie Test legend Shane Warne also made a public plea for both teams to move on from the tunnel tensions while condemning any form of personal attack on the cricket field.
Former England test captain Michael Vaughan, however, suggested Warner's rumoured track-record of aggressive sledging means there is no defence for his reaction to de Kock's reported taunt about his wife.
Australia captain Smith, however, said he believes Warner's angry reaction to de Kock's reported comment about his wife was completely understandable.
"Those things aren't on and you can't be getting into somebody's personal life like that," Smith said of de Kock.
"That's not on. It's crossing the line in my opinion. Right now it's in the hands of the umpires and the match referee, but we want to see the game played in a good hard-fought way and within the spirit of the game.
"As far as I'm aware I don't think (Australia's sledging of de Kock) was personal at all. But Faf can say what he likes I guess.
"That's my opinion — and what I've heard from the guys as well. I'm not 100 per cent sure but as far as I'm aware I don't think we got personal.
"I'm not going to make comment on (allegations Candice Warner was named). Next time you speak to Davey you can ask him I guess but what was said was personal and we don't want to see that happening anymore."
Du Plessis, who admitted he'd never seen anything like the incident in his career, called on umpires to take better control during games. "If you chirp each other it's always on the field. There needs to be boundaries," he said.
"Umpires play a big role in that, to make sure that you don't let it get to that stage."
Du Plessis had no issues with the tourists' sledging in the Test. "If I don't hear that then I'm disappointed," he said.
"I'm certainly not sitting here complaining about it. It's the way we play our cricket against them.
"I don't decide where that line is.
"Quinny's fine ... when you look at him now, it's like nothing happened." Smith made it clear that Australia's aggressive approach on the field would remain intact.
"We play our best cricket when we're aggressive, we're in the fight together, we're hunting as a pack," Smith said.
