The update is manual, but no need of FTP. Simply deactivating, deleting and installing the new is the best way of doing it 🙂
There is a safe update manual in the documentation, which you can follow if you want to: https://wpdreams.gitbooks.io/ajax-search-pro-documentation/content/update_notes.html
It mainly concerns updates from very old versions, but it does work with new ones as well.