Is the <div> 100% high at the time the Spltiter is created? If not, then the problem is not related to Kendo UI and you need to add some missing (100% or pixel) height styles to the <div>'s ancestor elements.
Here is a 100% high Splitter implementation that you can use as a reference.
the Telerik team
Join us on our journey to create the world's most complete HTML 5 UI Framework - download Kendo UI