The Millers have always had a friendly conflict with the Bantams going back to the days when former boss Ronnie Moore was a player in the 1980s and owing to the fact they have been in the same division for 12 of the last 13 seasons.
But following Evans' appointment last year the rivalry has heated up.
The 51-year-old was notoriously involved in an incident with a female steward at Valley Parade in 2012 when manager of Crawley, which the Bradford fans are not quick to forget, and it resulted in a six-match stadium ban for the Scot, who is yet to go to town publicly on his full discontent at that punishment.
He had the last laugh last term, though, as the Millers took six League Two points off Phil Parkinson's men, with April's 2-0 win at Valley Parade putting the South Yorkshire club on the brink of promotion.
Bradford followed in the play-offs shortly after and both sides have made an encouraging start to life in League One.
Evans believes all that will make for a special afternoon at New York.
"It's the tie of the round," he said. "How the television cameras aren't here is a mystery to everyone in football.
"But we understand in the early rounds that the lower league teams get the chance to get in front of the cameras.
"But this is the tie of the round - a Yorkshire derby, two teams doing well in League One, two teams on the back of a promotion last season, two fantastic sets of supporters and two great squads.
"It's got the hallmarks of a fantastic cup tie - let the best team win."