Open and launch the test case attached (NB project).

Click on the "setUserAgentStylesheet on Scene to Modena YellowOnBlack" button: the label on top becomes yellow, while it should stay red, because it was set to red at the USER (aka API) level.
Same thing for the SubScene.

Using Scene Builder, one can see (thanks to the CSS Analyzer) that the imported css are applied to the AUTHOR (aka stylesheet) level instead of the USER_AGENT level.