The Florida homestead exemption is not automatically applied. In fact Florida's homestead exemption has to be requested and the applicant and home must qualify for it. If you do manage to get this exemption there are benefits making it worth the effort.
Homestead qualifications are not to egregious and most who apply will end up getting the benefit. The application must be submitted between the dates of Jan 01 and March 01 of the current tax year. If your county accepts applications past that date you will most likely be registering for the next years cycle. When you purchase a home typically the closing agent will cover the application process and even provide you with some paperwork to assist you.
If you plan on the home being your primary residence for the next year then you will most likely be eligible. You do not want to apply if the home is intended to be an investment property. There are additional exemptions which you may be eligible for as well. Some types my be for disabled veterans, residents 65 or older, Blind residents etc.
Since those qualifications can change we suggest you contact the county tax appraisers office or a tax attorney for specifics. Just know that there are ways for many to lower their property taxes and help to protect their homes in this state. Thankfully there is a Florida Homestead Exemption.