The two were involved in an animated exchange after Wawrinka won the opening set, apparently over eye contact.
"What did you say? You're the one looking at me and talking to me. What are you looking for?" Wawrinka barked at Tsonga in French.
"Come on, let it go. Did I look at you once?"
Tsonga later preferred to keep it personal.
"Yeah, sometimes it happens. Sometimes it happens. We can talk during the game," he said.
"Nothing special, yeah. We just spoke about things that I think is only between him and me, and that's it."
Wawrinka admitted Tsonga - who made the final in Melbourne in 2008 - was always a tough customer to deal with, but said the on-court stress was normal for the latter stages of a slam.
"The beginning of the match was quite tense from both sides," the combative fourth seed said.
"We were maybe a little bit looking too much about what the other will do, waiting a little bit the other to do something on the court."It's not only a grand slam quarter-final, it's a tennis match."
"You can always have some tension. Everybody goes on the court to win the matches. Things can happen.
"But at the end there is no problem after the match."
Wawrinka, chasing his fourth major in four years, bulldozed through Tsonga after taking the first.
"It's never easy to play against him ... he's a strong player and the conditions were quite fast today," Wawrinka said.
"It was a little bit windy and (the ball) wasn't too easy to control.
"In the first set, I think I rallied a bit too much but then I started to move a bit better and be a bit more aggressive and I think that was the difference."
- AAP