Read more about how the Asset Pipeline works here: http://guides.rubyonrails.org//asset_pipeline.html
TL;DR: If you add an import statement to your application.scss to bring your posts.scss file into that parent (or have an import tree or similar that auto-includes it) then the SCSS that you write in posts.scss becomes part of the one-and-only compiled/minified/magically available EVERYWHERE application.css that it compiles into. There is never any different CSS on any page in your entire application. All pages get the same CSS and JS through the Asset Pipeline unless you did something very non-standard.
If you aren't seeing the effect you are after, after making sure all of the above is accurate, then you may have to also consider that the CSS selector isn't correct, and the browser is ignoring it since it does not apply to the actual page when it renders to HTML.