Smith will take charge of his first home game tonight, when Rhinos face Wakefield Trinity in what has become a relegation four-pointer.
Wakefield are 11th in the Betfred Super League table, one point behind Rhinos and have lost their last six league and cup games.
After being unbeaten in their last three home games - a draw against Huddersfield Giants and wins over Toulouse Olympique and Hull KR - Rhinos crashed back to earth last Sunday when they were crushed 23-8 at Salford Red Devils.
Today’s game is effectively the half-way point of the season and a loss to Wakefield would see the teams swap places.
Rhinos are only three points clear of basement dwellers Toulouse Olympique, but Thompson is confident Smith can turn things around and inspire a climb up the table, once his ideas have sunk in.
The defeat at Salford was Rohan Smith’s first game in charge, after six matches under interim-boss Jamie Jones-Buchanan.
Richard Agar, who began the season in Rhinos’ hot seat, resigned after just one win from their opening half a dozen matches.
Thompson said: “Having three different coaches in the last three months and three different styles, it takes a lot to get your head around that.
“I guess we just have to open our minds up again and make sure we buy into this new way of playing - this new way of defending and new way of attacking.
“We have been all over the shop with the last three coaches; Jonesy did an outstanding job over his six weeks and Rohan has come in and brought some fresh ideas.
“We just have to buy into what he is telling us to do and I think we will be all right.”
Thompson stressed Rhinos need to “get a feel for how he wants us to play and his expectations”.
He added: “We will be right, for sure - we just have to make sure our minds are open to the new style of play.
“I think getting your head around three different styles is hard.
“Everyone bought into Jonesy’s way of playing and we didn’t know how long he was going to be coach for.
“We just have to do the same thing with Rohan and we’ll be fine.”
“He has been really good,” he said of the new boss’ first weeks at the club.
“I like his mindset about playing freely and if you see something, take it.
“I really love that mindset.
“We will get the gist of things in the next month, hopefully.
“It will take a good couple of weeks to make everything stick and become second nature, but it is as cool how, how he coaches.
“It is different and I like it.”
Thompson joined Rhinos, initially on loan, in 2020 after Toronto Woklfpack’s withdrawal from Betfred Super League.
The 33-year-old Kiwi has spells with Gold Coast Titans, Wests Tigers and New Zealand Warriors in the NRL before moving to England with Leigh Ce turions and then joining Warrington Wolves.
After some impressive early performances for Leeds, Thompson signed a two-year contract which expires this autumn.
Rhinos have several players in a similar situation, including young back Jack Broadbent who is being strongly linked with a move to neighbours Castleford Tigers.
Smith has confirmed he is already beginning to think about the make up of his squad for 2023, but Thompson said his future is as yet undecided.
“We definitely want to stay in the United Kingdom for one more year,” Thompson stated.
“That is definitely on the cards, but there is no talk as yet about what or where.”
Thompson insisted the uncertainty is not a distraction.
He said: “What will be will be.
“It is just one of those things that will handle itself.
“It will get taken care of when it gets taken care of.”