The Rugby Park outfit will head to Easter Road for Sunday's Premiership encounter full of confidence following their 4-0 hammering of Hearts on Boxing Day.
The comprehensive victory took their current run to three wins from their last four outings and helped them move just four points behind the top six.
Johnston is aware that Hibs have been given a new lease of life and fresh steeliness reminiscent of Caley Thistle following Butcher's move from the Highlanders last month.
But, following the capital outfit's own 2-0 success against Ross County in Dingwall on Thursday, the Kilmarnock boss is keen to build on his side's resurgence.
He said: "Hibs are well organised, it will be the same as when Terry was at Inverness. They work hard for each other and they had a great track record with the team spirit that they had.
"They didn't lose a lot of goals and you can see that just now - they're not conceding many."
The win over County was only Hibs' second in their last 10 games, to go with two draws, and doubled their meagre goal tally during that run.
And Johnston saw that result as evidence of growing confidence under Butcher.
"Terry's obviously given them a lot of confidence as they've not scored a lot in the (previous) seven or eight games," he said. "That shows you the lift he's given them.
"It's going to be difficult but we've got to put a run of results together. It's not good enough where we are (in the league) but we've not been far away for the majority of the season.
"Maybe individual errors have cost us dearly. But we're always going to score goals, we just need to keep it tight at the back. That's why it was pleasing to get a clean sheet at Hearts."
Victories over Ross County, Partick Thistle and Hearts have eased the pressure on Johnston after a dismal opening to the campaign.
And the impact made by the club's youngsters, such as Chris Johnston and Rory McKenzie, who both scored against Hearts, and midfielders Craig Slater and on-loan Celtic youngster Jackson Irvine - all 20 or younger - have given hope for the future.
Johnston added: "Confidence is growing and you can see that in the young players who have come in.
"Craig Slater, Jackson Irvine and others - you can see the energy they give us. The young boys have come in and given us all a lift and you can see that with results."