I agree that Adam did not start "aging" (physical deterioration towards death) until after the fall...But how do you know that Genesis only accounts for Adam's post-fall days and his mentioned age of 930 years is not inclusive of his pre-fall days as well?
Prior to the fall, in Genesis 1:14, the stars, sun, moon and etc. ("lights") were given for the marking of seasons, days and years.
Given this passage, it is obvious that time was being tracked prior to the fall. This would indicate, to me, that Adam's 930 years are inclusive of the pre-fall days...It is his accurate age from the sixth day until his death.
It is a subject of interpretation. If you want to argue on it, I will concede since to me it is of no importance.