Hughes claimed second in a high-stakes snowboard cross final at the Winter Olympics on Thursday with Pullin, a two-time world-champion, crashing out in the decider to finish sixth.
Pullin left the course without speaking to or congratulating Hughes and Lipshut later confirmed there are long-standing issues between the pair.
“Those are personal issues they have,” Lipshut said.
“What we have done is put a process in place where they all respect each other as athletes.
“We’ve set up a process where they are happy to be on the same team here and they all get on well enough to do their sport – and that’s all we ask of them.”
Hughes has his own coach and largely trains separately to Pullin and a number of other riders in the Australian snowboard cross team.
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Things came to a head at the Sochi Winter Olympics over funding issues in the team, Hughes part of a group using the hashtag ‘team outcast’ on social media to express displeasure at the situation.
But Lipshut said those matters had been resolved and the team functioned well despite the divisions.
“No one crossed each other and the lead-up here has been respectful,” Lipshut said.
“We actually rehearsed the lead-in (to PyeongChang) for years. We said ‘you’re all going to be in the same team, you better get used to it’. He added with a chuckle: “I’m actually not going to say what my worst fear was.”
“In this sport, you need to be a very strong personality because it’s just dog eat dog out there. That’s the type of sport it is. If you want dog eat dog you need some big dogs.”
Hughes said he was extremely grateful to the Olympic Winter Institute for the new program developed since Sochi.
He said he wouldn’t be in PyeongChang if things had continued down the same path.
Asked whether he was unhappy that his teammates hadn’t hung around to congratulate him he said: “We’re an individual sport, we all want to beat each other. It is what it is.”
