I am attaching an MVC project, where the same scenario is demonstrated (Kendo MVVM with nested templates).
With it, the bindings work as expected when wrapped in a single container element. Having two or more first-level elements is going to result in an unexpected behavior. This limitation is documented in the following documentation example:
With the above mentioned modifications you will be able to bind both the DropDownLists and the Segment templates (demonstrated in the attached project).