I tried the same and it works fine at my end. Could you kindly check the attached sample and let me know your observations. If it works properly then modify it so that it replicates your issue and I can assist you further.
The grey space is for the content of tabs but I think, you want to use C1Tabs as tabstrip i.e with no content. So, in order to remove the grey space, you may set the Height property of the C1Tabs accordingly. Here is the code for same: