Question: I have updated a web page that I didn't create. I worked locally perfecting the new layout which was fine.

However when I moved it to the server, a lot of styles didn't apply. 

In troubleshooting, I found that the styles that weren't working on the server were listed as "Author Stylesheet" styles locally (in Safari Dev Tools). There are no inline styles nor is there a style tag in the HTML. The other external stylesheets show the name of the stylesheet with the line of where to find the style.

How can figure out what the source of the Author Stylesheet actually is?

Answer: 
I'm not sure if this is 100% accurate, but I believe that Safari will not show the name of the css file if it is named default.css. In my case, Chrome tools displayed the file name (not just "Author Stylesheet").
Wayne, I don't think you might declare the author of CSS file on it. You must passing the wrong name or locale from CSS server, is there all your CSS found? Aren't u using css on your local or .min.css in your app? User google chrome in the console tab to look wgat is the problems with your stylesheet.