Conor Clarence, 23, and 25-year-old Shane Frane - both from the Simon Community hostel at Bonds Hill in Derry - stand accused of a total of 14 offences and appeared in court in the city on Monday.
The court heard that Clarence, who faces four charges including aggravated vehicle-taking causing death, has admitted being a passenger in the stolen 4X4 which struck a police patrol car on Saturday.
He was said to have cooperated fully with the police investigation and expressed remorse.
"He wants to publicly express his apology and regret for the role he had in this tragic incident," his defence solicitor told the court.
Clarence's co-accused is charged with a total of 10 offences, including death by dangerous driving, driving whilst unfit through drink or drugs, failing to stop at the scene of an accident, and burglary.
Philippa was enthusiastic, bubbly and had a beautiful personality. She was just loved by her colleagues and she turned that love to the community she served.
Chief Superintendent Stephen Cargin
As the charges were being read out, both men were warned to keep quiet.
"I do not want to hear another word out of either of you. Stand there silently," District Judge Barney McElholm told them.
The court heard how keys for the stolen Land Cruiser were taken from a house in the Fountain Hill area. The 4X4 later jumped a red light, before hitting the unmarked police car on the Limavady Road.
Constable Reynolds, 27, was a rear-seat passenger on the driver's side. She was killed instantly.
District Judge Barney McElholm described her death as a "senseless and needless loss of life", and expressed condolences on behalf of the court to the young woman's family, friends and colleagues.
According to the prosecution, both defendants fled the scene of the crash and the passenger (Clarence) tried to conceal his identity by changing his clothes.
No applications for bail were made and both Clarence and Frane were remanded in custody to appear in court again on 7 March.