Thank you for the video - it really helps understand the issue.
In your case I'm afraid that some of your CSS is being applied to Kentico's element as well. The zones that you see in Page/Design tab are just standard HTML elements with some CSS being applied to them. Since the zones are placed on the same page as your own CSS/JS, its styles can be overridden.
Solution in your case would be to use Developers tools/Firebug to investigate which of your styles are being applied to Kentico zones and then make your styles more specific. So for example instead of having a style like:
which is very generic and is by default applied to each div you should have: