I examined the demo Tsvetie provided but I was not able to observe the problems you report - the panel gets shown, after that an ajax request is performed to load the splitter and after the ajax request ends, respectively the splitter is loaded, the loading image gets hidden. I also debugged the page and the break point in the Page_Load event was hit only once as expected and not twice as you report. In order to confirm this I added some code which counts the number of loads in a Session object - please see the modified demo in order to see what I mean.
In case the problems persist on your end, please provide more details on what exactly you mean or how to modify the code, since the very same code attached does not replicate the issues you describe.
the Telerik team