The three other men were named as witnesses in two cases started by the police following the shooting death of Sinha.
Senior Judicial Magistrate Tamanna Farah issued the 7-day remand order on Wednesday.
The RAB had sought 10 days to grill constables Safanur Karim, Kamal Hossain and Abdullah Al Mamum, and ASI Liton Mia, who are implicated in a case started by Sinha's sister Sharmin Shahriar Ferdous.
Although Safanur, Kamal, Mamun and Liton weren't placed on remand at the time, the RAB was given permission to interrogate them at the jail gate.
The elite police unit later applied to remand them in custody and the judge set Aug 12 for the hearing.
Meanwhile, the RAB also sought 10 days to question Md Nurul Amin, Md Nezamuddin and Mohammad Ayaj, who were named as witnesses in the cases started by police over the killing of Sinha and alleged recovery of drugs from his car.
But they, too, have been placed on a 7-day remand following their arrest from Teknaf's Baharchhara Union on Aug 10.