The 19-25 loss they suffered at the Reds' hands in March will be at the top of the memory bank.
But, hosting the Reds again in the quarterfinals, they will look to repeat last year's 29-20 win in Hamilton.
McMillan said, "When we play the Reds, we tend to bring out the best in each other. Both teams like to express themselves with the ball in hand, and we expect a fast-paced, fierce encounter.
"We have been impressed with how the Reds have been playing. They are clear on their identity, have threats across the park to impost their game on you. They look a cohesive, happy unit. They will be up for this game."
After losses to the two top teams on consecutive weekends, the Hurricanes and the Blues, the Chiefs are looking to home town support to have them at their peak for the game.
"We love playing at home and think we have the best supporters in the world. They have been magnificent turning up for us all year, even though at times our season has been a bit of a rollercoaster journey."
Hooker Samisoni Taukei'aho is back in the starting lineup with centre Anton Lienert-Brown and fullback Shaun Stevenson back after they missed the Blues game.
The Reds have decided to have Tom Lynagh run their game from the first five-eighths. He's become more familiar with the role and has started in eight of his 10 games this year.
Lawson Creighton was preferred as his substitute, leaving no room for James O'Connor to travel to Hamilton.
Coach Les Kiss said, "Tom's finals experience last year pays forward for us. With Lawson from the bench, it's a combo that's worked well for us this season.
"I'm confident in the job they'll do."
Former Hurricanes prop Jeffery Toomaga-Allen has returned to start, while lock Seru Uru will play his 50th game.
Kiss is well aware of the task ahead of the side.
"Winning in Hamilton will be a difficult task. If we commit to playing our style, we've got a chance against a good Chiefs side.
"We have had some positive results against New Zealand teams this season. Of the three wins, one was crucially in Christchurch.
"That experience, and what we've learned in close matches, will stand us in good stead, but it doesn't guarantee anything.
"We've got to be able to handle the purple patch they'll have in the game, and that's going to take a massive collective effort.
"I'm more than comfortable we have the players to turn up for those special moments in games like this."