When using binding to CheckState property and TriStateMode is enabled the checking of parent (its business object) does not affect unrealized childrens' CheckState, because the bindings have greater priority than the TriState logic. Same in the other direction - checking the child has no effect over the parent.

Marking this as Declined.
TriState Mode is supported in XAML-defined or code behind defined trees with direct creation of 3Viewitems. 
In DataBound scenarios, 3-State should be created by the user with ViewModels as described in this help article.

http://www.telerik.com/help/wpf/radtreeview-howto-tri-state-mvvm.html