To reproduce the issue, add a RadDock with one tool window, add a RadSchedulerNavigator inside that window, run the project and unpin/pin the tool window. You will see that the selected timezone has changed.

To workaround the issue, remove the AssociatedScheduler of RadSchedulerNavigator at design time and then add this code in the form's constructor:
            this.radSchedulerNavigator1.BindingContext = new BindingContext();
            this.radSchedulerNavigator1.AssociatedScheduler = this.radScheduler1;