flagrante delicto or hot pursuit ?

What is the difference between flagrante delicto or hot pursuit? Is there a specific time to be execute by flagrante delicto or hot pursuit.We had a case before of rape here what the story goes. A female student came to our office allegedly reported that she was rape by her teacher inside the classroom it happened 10:00am in the morning but she reported the incident to us at about 3:30 pm in the afternoon of same day. We went to the school and arrested the suspect and took the victim at the crime laboratory. The women's desk officer made the affidavit there were no witnesses . The fiscal told us we don't have any personal knowledge of the incident happened, it was unlawfull arrest he said. When we came to the crime scene the suspect was not inside of the said classroom instead he was at the principal's office when we arrested him. The fiscal made a resolution for his release. Is that case not a hot pursuit?

i agree with the prosecutor, but this topic is still hotly debated.