I think the problem is the theme. As you know, WP allows theme to add custom style to the editor. And that might affect the plugin's CSS. I'd suggest you add some small CSS to the edit screen to fix this issue. We've got a tutorial on doing this.
Hi Jackky, thanks for your investigation. I've added CSS to the MB Blocks extension and will release it in the next version.
Regarding refactoring all the markup, I'm afraid it's not possible due to a lot of unexpected affects and BEM has quite low specificity (usually 1 class), which still be overwritten by WP or other plugins/themes.