Understanding a Civil Demand

Just received my civil demand after a recent shoplift in NY. No cops involved. I sent the payment in the mail today, but I'm a little curious about the bold text:

IMPORTANT NOTICE: The payment of any demand upon you does not prevent criminal prosecution under a related criminal statute provision. Payment of the amount demanded may not be used in any court proceedings as an admission of liability.

Do I have to be alert of any additional proceedings now that I've sent the payment? Is this over now? And will I get any kind of verification from anyone that this is over?

Much thanks.

They are making it plain that if the police or courts are involved, that paying the demand won't stop a prosecution. If the police and courts are not yet involved, they probably won't become involved.