Usually, there are 2 themes being used on a Drupal site, one for the "public" side (default theme), and the other for "backend" content (admin theme). You have to figure out which theme you want your custom CSS to be added to.
In your question, the screenshot is showing a page through which new content is being added, and it seems by its design that the theme being used is one of the admin themes.
You are probably using the option
Use the administration theme when editing or creating content. You can find that option on the Administration > Appearance page
Asset Injector is most likely adding the CSS to the default theme, not the admin theme.
In your case you can turn off the mentioned option. This way you will see the default theme when creating new content, and get the custom CSS, but you may not be happy with the look of other elements on the page, depending on the form styles in your default theme.
Or you can check if Asset Injector has the option which theme to add the CSS to. If you can make it add to the admin theme you can continue to use the admin theme for creating/editing content.