Something does not sound right. Were you given a Notice to Appear or was there a police report for this matter. You may want to talk to an attorney in the area to discuss this.
Legal disclaimer: This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice nor does it constitute an attorney-client relationship. Thank You
It is possible that they could go forward on the $200 civil penalty and not turn the case over to be handled criminally but that would be rare. When I was a prosecutor I would frequently see people in court that paid the civil penalty and were surprised to find out that didn't close the case. My experience with the civil penalties are that they are often threatened but rarely carried out. They could sue you and collect either three times their actual damages sustained or at least $200 in damages plus reasonable attorney's fees and court costs. They would have to front the filing fee, attorney's fees, and cost of litigation all in a hope to get it plus $200 back. They can trespass you and if you return it would be a crime. Paying the civil penalty would be a great deal to resolve the case if you did what they say but no matter what Publix tells you if the state gets the case it is out of Publix's hands and up to the state. An attorney can make sure your rights are protected but would likely cost more than the civil penalty.