You should ask the clerk of the court for the traffic court listed on your speeding ticket if police officers in these cities are allowed to write a ticket out of their jurisdiction. It may be that the cities work together and have an agreement since they are located next to each other.
In general, law enforcement is usually allowed to follow you out of their city limits if they see you commit an offense in their city but you are traveling in a manner that allows you to leave their jurisdiction or city before they can stop your car and cite you for the violation. So if you were speeding within Wilton Manors but by the time the police officer stopped your vehicle you had traveled into Oakland Park that normally would be allowable.
You are issued a ticket by the State of Florida and not by the city. If the officer is certified by the state then they typically have the "authority" to write the ticket.
To find out for certain if what occurred in your situation was allowable by city, county and state laws ask the court and perhaps contact a traffic lawyer. If you want to fight this ticket in court then the county clerk or lawyer should be able to tell you how to do so.
If this speeding ticket affects your insurance rates then you can get a quote for low cost car insurance here.