The Wallabies overcame a stubborn, defensively sound Georgia 27-8 at Shizuoka, two late tries for the men in green and gold giving the scoreline some added gloss after an error-strewn clash.
Wales' 27-19 win over Fiji on Wednesday had already guaranteed Australia a place in the last eight, with the Welsh playing minnows Uruguay on Sunday in a match that should see them book the Pool D winners' spot.
That sets up Cheika for a crack at former teammate Jones, who thanked the "typhoon gods" after England's final Pool C game with France was cancelled over incoming Typhoon Hagibis, giving them extra time to prepare.
"They better win, they've had the best preparation according to the coach," said Cheika, adding that his team were already licking their lips at the likely prospect of taking on England at Oita next Saturday.
"They'll be really looking forward to this contest, you can see that in the dressing room already," Cheika said.
"The only relevance is Saturday. All the different things, who's had a week on, who's had a week off, who's been resting, who hasn't, it all comes down to kick-off."
Cheika said it was useful for his team to be tested and made to work against Georgia ahead of the knockout round.
"The hit-out was good, having to dig in, work hard, get up off the ground, get into some tough stuff," he said.
"It's how we wanted the game to go, we wanted to work like that."
He added: "Our forwards stepped right up to it. We handled the Georgian scrum well, we scored a maul try... and the line-out worked.
"It was a good hit-out for the forwards, they got a good shift in. They're getting the bit between their teeth."
Cheika admitted his team were guilty of several handling mistakes but warned that he expected them to be more accurate next week.
"We did drop a bit too much ball," he said. "But I thought our carrying was strong, we just didn't have the finishing touch on a lot of stuff so we'll definitely put that on and we'll prepare that and be ready to finish the opportunities that will come next weekend."
Milton Haig, in his final game with Georgia after eight years as head coach, said the huge tackle count - almost 80 in the first 20 minutes - had tired his team.
"We knew it was going take a toll in the second half," the Kiwi said.
"We had some opportunities in the second-half, but we couldn't get our set piece going.
"I can't fault the boys on how they put themselves about. I was really proud of them tonight, especially in defence."
Australia, Haig added, were "a very good side".
"We played pretty well and if they get a slating (for handling errors), that would be disrespectful to Georgia."
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