The rumor that Florida does not extradite is false. Florida extradites aggressively and does not limit that pursuit based on distance or state lines.
Felony warrants including probation violation warrants are pursued by Florida regardless of where the person is picked up. Alabama, Alaska, or anywhere else, Florida will send transport officers to collect someone on an active felony warrant. The state has a well established extradition process and treats probation violations seriously, particularly because a violation represents a breach of an agreement the court already extended as a form of leniency.
The practical timeline varies. Once Alabama notifies Florida that they have someone with an active Florida warrant in custody, Florida has a window to respond and arrange transport. That process can take anywhere from a few days to several weeks, depending on how quickly Florida's extradition unit processes the request and schedules transport officers. During that window the person sits in Alabama custody on the Florida hold.
There is no realistic path to avoiding extradition on a felony probation violation warrant. Attempting to fight extradition through the courts is expensive, time consuming, and almost never successful for a straightforward warrant situation. The more productive use of time and resources is getting a Florida attorney involved immediately to communicate with the probation authority and the court, assess what the violation involves, and begin building the strongest possible case for when the person is brought back before the Florida judge.
Cooperating with the process and having legal representation in place in Florida before arriving is a significantly better position than fighting extradition and arriving without counsel.