Theme Custom Options – No Update

This may be the 100th time this subject has come up, I am sure.

Instatllation:
– Fresh Hostgator Account.
– Fresh WP 4,2,2 install.
– Twenty-Fifteen Theme.
– Wp Super Cache uninstalled.
– Chrome Browser viewing site with Dev Tools running and Cache Disabled.

Me:
– Many years software in software development.
– However very little on web technology – No Php, no WP.

When trying to customize the theme using the Dashboard theme customizer, it seems that it is the style.css that is being cached somewhere and not updating. I see it in the files downloading in the Dev Tools, but its content is never altered. Content updates just fine.

Changes to things like the background colors persist in the customize settings but won’t even stick in the preview panel, let alone another tab with the site being displayed (with hard refresh).

I would like to fix this in a way that causes the styles to update on any change. I saw a fix for adding the version on the end of the path to the style.css file that is generated off the filedate of the style.css file. This seems like a good solution. As I am doing this by just reading an editing the installed files, I don’t have a way of tracing what php files are called during the rendering of the home page.

And so I have two questions:

1) Does the theme customizer actually edit the theme’s style.css file?
2) What php file is responsible for rendering the link to the css files in the output?

Thanks in advance.