The pair who were shot remained at Sydney's St Vincent's Hospital on Sunday having undergone surgery.
They were listed as in a serious but stable condition.
Internet video footage of the incident shows at least one of the teenagers being rushed away on a stretcher while two bullet holes are clearly visible on the front windscreen of the battered silver Honda.
Other footage shows a police officer appearing to punch one of the teenagers as he's pinned to the ground. The youth is then dragged onto the pavement, heavily bleeding and handcuffed.
It's not clear if the teenager being punched was one of the two who were shot.
Police have launched an internal investigation into the incident, including looking at whether officers were correct to open fire at the car and their use of force.
Mount Druitt man Matthew Dalton appeared at Parramatta Bail Court on Sunday accused of being one of those inside the car.
The 24-year-old was charged with being carried in conveyance and appeared in court via an audio-visual link from Surry Hills police station.
Magistrate Michael Morahan formally refused bail and Dalton is due to appear at Sydney's Central Local Court on Monday.
Two other boys, aged 14 and 16, who are also alleged to have been passengers in the car appeared at Parramatta Children's Court on Sunday.
Both are charged with being carried in conveyance and cannot be named for legal reasons.
A 13-year-old boy also accused of riding in the car is due to appear at Bidura Children's Court in Sydney in May.
-AAP