This is not legal advice, only my interpretation of the law and experience in Florida specifically the 5th district. 

I was recently asked about the legalities of detaining you to issue a trespass. Since I had been trespassed from a public place and refused to provide identification based off of the Florida statute 901.151 (stop and ID statute) I know this all too well.

Florida has no criminal statute that directs or otherwise allows officers to detain you for to issue a trespass warning, only if you are trespassing after warning.

Terry v. Ohio allows for the detainment if a criminal offense has been, is being, or is about to be committed. Many states have statutes that direct police officers when they can detain for an investigatory stop.

The 3 Types of Police Encounters in Florida: 

• Consensual – Consensual encounters of law enforcement officers and citizens involves consent.
  
  

• Investigatory Stops– Investigatory stops occur when an officer may reasonably detain a citizen “temporarily” but only if the officer has reasonable suspicion.
  
  

• Arrests (either verbal, written or physical).

Absent of any other criminal charge or articulatable suspicion, I do not see why a police officer can detain you to issue a trespass warning. The act of being told to leave, and leaving is not a crime. Entering or remaining on the property after being told to leave is where the FSS is violated and now a criminal offense is committed.