yeah, the STYLE tab info just gets copied over to the STYLE tab of the new skin, not flattened to the file system.
So best option.
* Copy all the css from the VIEW CHANGES tab.
* paste it into /skins/YOUR-SKIN/css/overrides.css
(a new file you create)
* open /skins/YOUR-SKIN/include.php and add
jrCore_register_module_feature('jrCore', 'css', 'xxYourSkin', 'overrides.css');
to the BOTTOM of all the other .css files registered there so it gets added last to the compiled css file.
* Upload that and reset the sites caches.
Not perfect, but beats adjusting the existing CSS files one by one with each change. Then just go forward with the file system option going forward.
(Not a great fan of the STYLE tab, but it does make it easier for those unfamiliar with web techniques to do basic adjustments so its necessary)