Hi Pavel,
Thank you for contacting Syncfusion Support.
We have analyzed your query and modified the sample that tries to meet your requirement. In this sample, we have changed the Focusable of the TabItem as false and it will allow the TextBox to get focus on SelectionChange. We can change the Focusable property of TabItem by applying Style to the DocumentTabItem. Please download the modified sample from the below location.
Modified Sample:
DockingManager_TabItemFocus_SampleRegards,
Durga S.