Australian Cheika was coach of the Wallabies between 2014 and 2019, but after initially taking on a consultant role, took over Argentina fulltime in March.
He masterminded a seven-try romp for his side against a depleted Wallabies, Argentina's biggest ever win over Australia and their largest in the Rugby Championship.
"I love these guys, they're my crew now," Cheika said. "I was up on the last try, cheering. But then I started crying because I know I probably shouldn't be doing this. It was a bit confusing for me, personally.
Argentina will now head to New Zealand for two further Rugby Championship tests, the first of which is in Christchurch on Aug. 27. Each team in the competition, which also includes South Africa, has won one game after the opening two rounds.
"It's good to be going to Australia and have a few days off, seeing my mum and my brothers and sisters and take the boys for a Leb (Lebanese) feed at my mum's place," Cheika said.
"But I am looking forward to going to New Zealand because it is a great place to go and play rugby."