Apply your theme styling for content
When you include CKEditor or TinyMCE with N1ED to the page, you expect that content inside the editor will look exactly as it looks on the website, that is preserving styles of buttons, margins, fonts and so on.
If your editor works in the inline mode this happens automatically. But if you run TinyMCE/CKEditor in the standard mode, then technically the content displays in the separate iframe, and styles of the page cannot apply to it.
Nevertheless, in N1ED you can apply website styles to the content inside the WYSIWYG editor. Since styles are stored in CSS files, the solution is to include them to the content as well. To do this, just go on the tab "Content theme" in N1ED configuration and add there CSS styles files you use.
You can also connect various JS scripts to the content. Carefully check each JS file you add not to break the editor. Usually adding JS files it not required in content area to style a content.
If your website uses Bootstrap, and you want to connect its styles too, so just enable Bootstrap Editor and all the styles of Bootstrap 3 or Bootstrap 4 (according to option you choose) will be added automatically without any actions from your side.