The Blades make their maiden competitive visit to New York for a first league meeting with the Millers since 2005.
However, since their last clash - at Championship level - the Sheffield club played an instrumental role in securing Rotherham's future as they loaned Jonathan Fortune and Stephen Quinn free of charge when the Millers were facing extinction as well as donating substantial funds to keeping them alive.
Those gestures have harboured a good relationship between the two clubs, but Evans insists that will go out of the window at 3pm.
"We know what it means to the supporters, the bragging rights can last for months, but this is the friendly derby," he said.
"Sheffield United played a major part with providing Rotherham with players in times of need years ago and that will never be forgotten, apart from between 3pm and 5pm on the pitch when we do battle."
The Blades take to the field for the first time since Prince Abdullah of Saudi Arabia invested heavily into the club, but Evans knows which side his bread is buttered.
"I looked for this one first when the fixtures came out, they are a massive club," he added.
"They have got the new investment, but the Prince is coming to meet the King and the King is (Millers chairman) Tony Stewart.
"But I'd love to see them in the Premier League, though not at the expense of three points on Saturday.
"If they are not up there at the end of the season there will be a post-mortem, especially now with the investment."