There was an almost palpable sense of relief in the Irish camp on Sunday when Keith Wood's team inched home to a 16-15 win over the Pumas in Adelaide. In doing so, they drove a stake through the heart of the team that eliminated them from the last World Cup in an equally dramatic match in Lens, France.
Jones summoned up another ghost from that tournament when he predicted Saturday's match would be played with full-blooded intensity by the Irish, irrespective of any suggestions by O'Sullivan that he might rest some of his bruised and battered heroes from Adelaide to freshen them up for the quarter-finals a week later.
"He's a cagey character, isn't he?" Jones said of O'Sullivan. "They've always got smiling eyes, the Irish, haven't they? And I think they're smiling at the moment. But we fully understand their intention on Saturday is to play as physically and aggressively as Ireland normally do.
"You've just got to go back to the (Australia-Ireland) pool game in 1999 and watch some of the incidents in that game and that's what we're expecting on Saturday. Full stop."
In fact, it was more of a comma because Jones went on to stipulate he was not expecting any repeat of the niggle that led to a ferocious blow-up between Toutai Kefu and Trevor Brennan, the Australian number eight pummelling the Irish flanker after being rabbit-punched on the ground.
"We're not saying Saturday's game is going to be spiteful but we're saying it's going to be physically aggressive," Jones said.
Certainly Kefu doesn't anticipate a repeat of the sly play that provoked him to breach strict protocol forbidding retaliation at Lansdowne Road on October 10, 1999. "It could turn out like that but I hope it wouldn't," Kefu, who was handed a two-match suspension, said.
"It would be a waste of time if Ireland did that. They've got some wonderful players there and if they put their thoughts to it, they could really take this match to Australia. They beat us last year at Lansdowne Road without any of that nonsense."
The Irish will announce their team today and although there will be considerable significance attached to the selection or omission of such greats as centre Kevin Maggs and number eight Victor Costello, what will truly signal Ireland's approach to this game will be O'Sullivan's choice of hooker.
If it is Shane Byrne, the Australians will know they are in for a hard game. But if it is Wood, the Wallabies will know this is war.
Wood has grown into a talismanic figure where Ireland is concerned and the Wallabies are well aware of the significance he - and to a slightly lesser degree fellow British Lion Brian O'Driscoll - hold within the side. So revered are they that none of their team-mates would dare give anything less than his best in their company.
However, Jones is well aware that there is far more to Wood's team than passion, aggression and a determination to stand shoulder-to-shoulder, answering Ireland's call.
"They're an enormously intelligent side," Jones said. "They play very much to their strengths and they've worked out a game plan to suit the resources they've got. They're tactically astute for each game they play."
If they are so astute and have - in Jones' mind at least - decided on an approach of physical confrontation, it follows logically that they must view the Wallabies pack as a weakness to be exploited.
"I think historically they probably do," Jones said.