The Cherries are riding high at the top of the Championship and the Millers’ boss feels the visitors are big favourites for today’s tie.
Evans, who has confirmed that Kirk Broadfoot will resume full-contact training on Monday, said: “We have the luxury of playing the league leaders at home – they can play three teams and we have lost four players.
“But the FA Cup is always magical and we know before a ball is kicked that there will be five or six surprise results around the country which will make people’s eyebrows lift.
“We have to be one of them because there is no one outside the town of Rotherham who is expecting us to be beating Bournemouth.
“They are beating teams for fun at the minute whether it be home or away.
‘Okay, we wouldn’t have picked Bournemouth but Bournemouth wouldn’t have picked Rotherham. Ideally we want to keep our unbeaten run going and ideally we wouldn’t pick a Tuesday night to be travelling down to the South coast if there should be a replay although they tell me it’s warmer down there.”
Evans, who has seen Emmanuel Ledesma and Tom Lawrence return to their parent clubs, says the club are targeting some “big players” in the January transfer window to boost their numbers for the run to the end of the season.
He added: “There has been a lot of work going on in the last few weeks and it will start to get serious when we get Saturday’s match behind us.
“We have targeted some big players and we probably need to pursue three or four.