I'm not sure that I understand the distinction, or that I know what the "Augustinian constuct" of original sin is.
I think that original sin is the condemnation to death, "the way of all flesh", and that one of the "ways of flesh" is a tendency for the flesh to lead the immortal spirit into acts of corruption (actual sin or intentional sin).
So, to put it in broad life terms, the debt for original, contracted sin is paid for by physical death. Original sin does not carry with it the sense of moral blame: it is simply a fact, and a mystery. After death, the soul faces the consequences of its intentional sins, unless those sins are forgiven by grace.
I really don't know what Augustine had to say on the matter, but that's my belief. Did he differ?
In a real nutshell...St. Augustine taught that we inherit the guilt of Adam's sin (in fact through the act of procreation). Augustine wrote in Latin in the 4th century and seems to have been influenced by Tertulian. When his works were translated into Greek around the 14th century, the East rejected the formulation of inherited guilt, retaining the by then tradtitional belief in the East that only the consequences of Adam's sin were inherited, that each person's sins were theirs alone. The doctrine of original sin as seen by the Augustinians is the basis of the Roman dogma of the Immaculate Conception.
If you went to Catholic school a long time ago, the nuns used to teach that a tiny baby which died before baptism couldn't go to heaven because of original sin. The baby's soul went to a place called "Limbo". There was even a prayer for the souls in Limbo. It was a place where otherwise sinless souls went because a soul corrupted by original sin couldn't be in the prescence of God, though this place was not Hell. Original sin was viewed as a blot on the soul, very much a sin carried by a human being even though that human being had nothing to do with it. The soul was washed clean in Baptism.
The Church in the East has never held these views on original sin.