Ben Pringle got the show on the road for the Millers after just 64 seconds and leading marksman Daniel Nardiello added a second after 28 minutes of Tuesday night's League Two clash at the New York Stadium.
A third followed two minutes later from Michael O'Connor and Craig Morgan added the final touch seven minutes into the second half with his first goal for the club.
Exeter's consolation came from Danny Coles 14 minutes from time.
"I might watch from the stands again on Saturday," a delighted Evans said after the game.
"When we score first we normally do that to teams. When we score first we are normally very good because confidence rises, but it shouldn't be about confidence here because the one thing we have got is good players. What we ask them to do is work hard.
"We got the early goal and that set us up and when Daniel Nardiello works as hard as he did in the first half you would always pick him and he answered my criticism in the right way.
"I had a chat to him on Monday and he knew why he wasn't in the team on Saturday because his form has dipped, but he has answered that here and put the pie right in my face and that's a great reaction, that's what I want from my players.
"It was a stunning goal he scored, but Daniel is capable of that and that's never, ever in question."