City of God Against the Pagans

I think you are right- Augustine is using the words 'manners' here to designate somethink along the lines of the conduct of men. Augustine suggests Socrates may have wanted to establish a more definitive way to attain the blessed life. Thus, unlike philosophers before him who were concerned solely with 'causes', Socrates "though they[the causes] could only be comprehended by a purified mind." The 'manners' has to do with this 'purified mind' more than anything else. and the purified mind leads to a freedom from lusts, confusion, etc. More than just intellect, it influences the body, soul, and will as well.