Hi Stergios,
Thank you for contacting Syncfusion Support.
We have checked your sample by selecting items at runtime using Select method. As per the behavior of TreeNavigator control, it moves level by level to bring the SelectedItem into view. Items will be generated once the Parent container item loaded. So we couldn't select the third level item directly. To select the item from third level, control should navigate to first and second level one by one. So click the button twice to get the third level as SelectedItem in this sample and you can download the modified sample from the below link
Sample link:
SfTreeViewNavigatorSamplePlease let us know if you need any other assistance.
Regards,
M.Sugapriya