Millar suffered a less severe head injury and the Parole Board, at a hearing last month, noted it was his third such knock.
It was revealed the prisoner had been involved in another alcohol-affected smash in November 2016 for which he received diversion.
''Two incidents of alcohol-affected driving in such a short time ... indicate in our view serious underlying issues that require the concentrated focus of the drug treatment programme [DTP],'' Parole Board panel convener Judge Neil MacLean said.
Millar had recently started that course after already undertaking the short rehabilitation programme (SRP).
Defence counsel Fiona Guy Kidd QC told the Parole Board her client could be released now and continue the counselling in the community.
Millar told the board the therapy he had done so far gave him ''a fair idea'' of the effect of drugs and alcohol and that he had learned his lesson.
The board disagreed.
''There are fundamental underlying alcohol abuse issues that need to be got to grips with that would not have been covered simply by participating in the SRP, and warrant the intensive treatment provided by the DTP,'' Judge MacLean said.
The Sharma family met the Parole Board before the hearing with Millar and voiced their concerns about him returning to Alexandra, where the incident took place.
They also continued to feel stung that the Millar family had not met with them.
Guy Kidd said her client's family had tried to explore the option of restorative justice.
Judge MacLean said the communication breakdown reflected the ''understandable agonising effects on two families through one night's stupidity''.
Millar, the board heard, had accommodation awaiting him on release as well as a firm job offer.
He was also awaiting the result of a Court of Appeal decision.
Guy Kidd had argued for a shorter sentence, saying the judge did not give adequate consideration to Millar's youth and remorse.
His sentence end date is December 2021 at present.
He will appear again before the Parole Board in November.
