The hard-running Saracens number eight scored England's try in their series-levelling 25-17 win in Brisbane.
Returning to the squad after a 15-month absence, Vunipola has reminded head coach Jones what he can do.
"Billy is getting fitter. He has a while to go but we are pleased with his progress," said Jones.
"We picked him on the back of his improving club form and he's got better, and with us he is getting fitter and his commitment to be the best player he can be is improving too."
Vunipola, a stalwart of the 2019 World Cup final team, had to come to terms with being dropped after the 2021 Six Nations when Saracens were playing in the Championship.
"I was binned off for a year because I wasn't performing up to the standard," he said.
"There were two number eights playing better."
He was back to his powerful best last season and caught the eye with his performance for Saracens in the Premiership final.
With Alex Dombrandt and Sam Simmonds both unavailable to tour because of injury, Vunipola was recalled to the squad and won his 61st cap in the first Test defeat last week.
Disappointed with their performance as a pack, England bounced back impressively in Brisbane with Vunipola to the fore.
"We were hurting a lot from last week," he said. "The Australian pack beat us up there up front, especially towards the end of the game.
"It was on us as forwards to get front-foot ball. We did that and our mauls and scrums were different level.
"We want to come out next week and be better than we were this week. The first half, especially the first 35 minutes, I thought we were pretty good but we let them into the game."