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 the two clubs 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 keen to remind him of.
That altercation resulted in a six-match stadium ban for the Scot, who has yet to speak publicly of his dismay at the punishment.
Evans had the last laugh though as the Millers took six League Two points off Phil Parkinson's side last season, with April's 2-0 win at Valley Parade putting the South Yorkshire club on the brink of promotion.
Bradford followed Rotherham into League One via the play-offs shortly after and both sides have made an encouraging start to life in the third tier.
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."
There are 28 non-league clubs bidding to edge one step closer to a potential third-round jackpot when the Barclays Premier League big guns enter the competition, while the second-round draw is assured of four minnows in the hat.
Southern League Premier Division sides Corby and Biggleswade Town take on Dover and Stourbridge respectively, Kidderminster play Sutton United and Dartford travel to Salisbury.
Skrill Premier side Southport are hoping to avoid the runaround at Russell Slade's rampant Sky Bet League One leaders Leyton Orient, but League Two pacesetters Fleetwood face a potential banana skin at Skrill North side Gloucester and in-form Gateshead fancy their chances of an upset at Oxford United.
PE teacher Alex Sykes, manager of the lowest-ranked side left in the competition, Shortwood United, will have a little bit longer to prepare for the biggest team-talk of his football career as his side travel to Port Vale on Monday.
Shortwood, fifth from bottom in the Southern League Division One South & West, have already hit the jackpot as their tie will be screened live by BT Sport, thus ensuring a £67,500 windfall for a club residing in the eighth tier of English football.
Uwe Rosler's Brentford will be playing for more than a place in the second round as local bragging rights are at stake when they take on non-league neighbours Staines Town, while Skrill Premier promotion-chasers Grimsby entertain Scunthorpe in another derby clash.
Nigel Clough will attempt to kickstart his new club Sheffield United's season at Colchester, Wolves clash with Oldham at Boundary Park and form team Hartlepool take on Notts County in another all-League One affair.