The application’s assetManager is the component that is intended to be used to publish assets that come with extensions. So, any extension should use code like this:
// guess we're in your views folder
$filepathExtensionImages = dirname(__FILE__) . '../assets/images';
// assetManager will publish the folder and return the url to that folder
$baseUrl = Yii::app()->assetManager->publish( $filepathExtensionImages );
// use one of the images
$urlImage1 = "$baseUrl/image1.jpg";
echo '<img src="'.$urlImage1.'" />';
You can also publish your images one by one, instead of publishing the whole folder.
I’m not sure to which methods you refer. If I look at CWidget’s API, I can’t see anything related to assets.
Does the yii-debug-toolbar extension come with some helper methods related to asset publishing? If so, I guess the author of that extension could best explain how to use them.