Stylesheet overriding in Child theme

Generally speaking, you want to load your general stylesheet (style.css) first and follow it with your more specific stylesheet(s) (style-premium.css). However, the actual details of how CSS cascades are more complex than that and your specific stylesheet can still be overridden by the general stylesheet:

  • if the !important declaration is used
  • based on the specificity of individual selectors

You can learn more about how the cascade works via W3.org or this CSS tutorial, which even deals with your question directly:

It’s also useful to note that external stylesheets placed underneath
each other also cascade — that is, the styles in the lowest stylesheet
overrides those in the higher stylesheets.