I would have thought that the reasoned Atheist is a sufficiently rare beast that the evangelist neglects their existence.

I think there are plenty of people who basically do not question the recieved wisdom of the existence of God, but at the same time don't give the concept much time or headspace. These are the people the evangelist is after, people whose dormant belief in a God can be inspired into a more active one, following their faith.

Someone with an active belief system is a much tougher deal for an evangelist. As an experiment, during a time that our area was plagued with evangelists, I would attempt to repel evangelists by claiming all sorts of beliefs, to see which would be the belief they'd least like to tackle. Of those I tried, I found the best way to repel them was to claim to be a devout Catholic. Atheism, they were much more happy to tackle, but seemed to believe that an Atheist was either agnostic, or some sort of fallen, disillusioned Christian who could be restored to the light. The idea that someone might have an honest conviction that the whole religion business was too unlikely to contemplate just wasn't in their worldview.

people whose dormant belief in a God can be inspired into a more active one, following their faith

Hence "born again".