I checked the attached configuration of RadColorPicker in the major supported browsers and I did not notice displacement in the textboxes of the control.
Please ensure that you have provided the correct configuration of the color picker, because the one you posted will display only the Web Palette and the mentioned textboxes should not be visible at all in this case.
I would suggest checking for global CSS rules or custom style sheets that may be changing the position of the textboxes. To do so, follow these steps:
Remove all custom CSS from the page to verify if this is the cause for the problem. This can be done with commenting or deleting the references to style sheets and inline styles like in the example above.
Clear the browser and ASP caches to make sure the content is fresh. Reload the page in the browser completely (usually Ctrl+F5).
If the issue is gone start re-adding the custom CSS piece by piece to find the offending rule and make it more specific (e.g. add a class).
If this does not help, I will need a fully runnable sample that isolates the problem in order to inspect it locally and provide a more to the point answer.
Check out the Telerik Platform - the only platform that combines a rich set of UI tools with powerful cloud services to develop web, hybrid and native mobile apps.