First, be sure that you text, in the editor, don’t have any code from where you are copying it. Use the HTML tab to check that. In the link you provided, the text has paragraph, with span inside, with more span inside that span. Is kinda weird.
Beside that, you have to use CSS to style every detail of the text, like to ‘foresee’ what the user will use. Create style for paragraph, headers, span, bold, italic, whatever you need.