When you cut and paste from another source you're copying the style as well and if that style differs in Auctiva's editor or Auctiva doesn't have a matching style it won't show correctly. This is common across other platforms not just an issue with Auctiva.
What I do is after pasting my text, I highlight everything and change the font size and type to what the majority of the page will be using. Then go back and make changes to headings and stuff.