What they implied in reason was the awareness of Divine source for the universe called sometimes the natural religion (as opposed to the revealed one). Atheism was for them foolish and not reasonable.
That is why the rationalistic Deists can see the natural rights as self-evident.
They will say that moral sense arrose because a person with moral sense is more likely to get along with others in his community, and is thus more likely to survive and pass on his genes.
The problem with such a position, of course, is that falls victim to the naturalist fallacy: just because a moral sense evolved (and it probably did, BTW) does not mean that one ought to follow it. Their explanation is descriptive but not prescriptive. But the atheists I know don't really worry about this and treat their moral sense as if it were prescriptive anyway.