For the files included when you get a .zip from the Saratoga-Weather.org - Website Templates - AJAX/PHP - Updates tool, you need to follow the recommendations for each file. Most are replace old with new. Some are copy settings from old to new. The individual file recommendations are listed in a README file included in the .zip.
For third-party software (like the alternative dashboard), you’ll need to check each .php file for settings and copy those settings to the new scripts before upload. The third-party scripts are not checked by the version checker tool.
See Saratoga-Weather.org - Website Templates - AJAX/PHP - Maintaining your website for more info.