Both were among the World Cup players still involved in New Zealand, who took part in a two-day camp in Auckland this week.
McKenzie said, "It's about owning our stuff throughout the year. There are expectations for us as All Blacks to go back and perform for our Super team and to make sure we're doing that throughout the year and leading by example for the rest of the players coming through."
Jordan, who has been part of Robertson's successful Crusaders side, said Robertson appeared unaffected in his new role.
"Razor's his own man. He's not someone who changes for the environment he is in. He knows it is a step up and different from what he's experienced in the past, but he's content with the person he is, how he wants to behave, and how he wants to inspire people.
"I'm sure that he will do that throughout his tenure, and there'll be pretty similar stuff happening."
McKenzie said it had been a low-key camp, especially with the first Test match against England so far away. It had been a chance to catch up with other players and get a feel for Robertson and his new management team.
McKenzie had him as a coach when playing for the New Zealand Under-20s and the Barbarians in 2022.
But so far as he is concerned, it is about having a good Super Rugby Pacific campaign and putting his hand up there first so that he and the other players would be introducing themselves again later in the year.
There was no discussion about what position he might be required to play during 2024. Instead, he had concentrated on coming in and trying to achieve good numbers in the tests the players faced.
But, he had talked with various members of the coaching group in the past.
Will Jordan said it was the same for him. He had played a lot of rugby at fullback for the Crusaders, but the initial part of the season was about having a good Super campaign to hopefully make the All Blacks and see what happened from there.
He had put the disappointment of a second place at last year's World Cup behind him.
"There was a patch of the summer where you spent some time thinking about it. It probably took a while to get over it or have a bigger picture look at it, but now I am reasonably refreshed about heading back into footy.
"It was certainly a pretty awesome experience over in France. I learnt a lot and enjoyed the whole thing. As a group, we haven't touched on it too much. There's a new management group, and there'll be some new players coming in in the new year, so I'm looking forward now."