I’m not sure exactly what you’re asking? Can you give us a bit more detail on your question/issue? The 2 links you added don’t show up.
Also, do you have link to your site where this is taking place so I can take a look and see exactly what all is going on?
Anytime the Chrome tools/Inspector shows CSS code with (index) and not a link to a style.css or other css file, then that means the code comes from a different source that adds the CSS directly to the page and doesn’t come from a CSS file. Example, if you add some CSS code from the Genesis Theme settings page, it will show up on your site, but since it doesn’t have a file source it will say (index).