In terms of a Christian outlook of the world, that definition makes sense because it touches on an immaterial aspect of human beings, namely, that we have souls which utilize the intellect to make rational connections to come to conclusions about the world.
However, in terms of an "atheistic" outlook on the world, where there are no invisible entities like concepts, souls, or God, that definition is nonsense. There can be no such thing as "mental faculties," "assumptions and premises," or even "cause and effect" in an "atheistic" worldview because each of those things are immaterial in nature. You can't use the five senses to ascertain those entities, after all, but "Atheism" tells us that we only need our five senses to come to truth.
So, "atheists" cannot agree with the definition you provided unless they use another worldview to make sense of the nature of reason, for reason is not made of matter. Of course, that worldview is Christianity, and Christianity is the only worldview that makes sense of reason because reason cannot justify itself (which would be a logical fallacy of reification). It comes from God and reflects His thinking.
Philosophically speaking, "Atheism" cannot justify reason in any way, whether it appeals to a priori assumptions or empirical methods based on experience. At its foundation, "Atheism" starts from irrational premises and tries to argue to rational conclusions. The American "Atheists" are just being arbitrary when they tell people to "celebrate Reason." Their own worldview makes reason anything from eating hot fudge sundaes to using laws of logic. There is no objective way, in an "atheist" universe, to determine what is the best utilization of reason because it makes it all relative, in the eye of the (evolutionary) beholder.