Yes, node-level events are fired during LoadPostData control execution lifecycle stage.
There are some reasons for such behavior. One of them is that it is impossible in some cases (node removed, changed its various properties, etc) to fire node change events in RaiseChangedEvents . For example, node was checked and then it was deleted from treeview. So how would you handle this scenario. It means that you need to know what was current treeview state (when this node event was logged at client-side).
So all these node events fire during LoadPostData synchronously with application of all client-side changes to treeview state (expanded, checked, removed, inserted, etc.)
As far as I understand your problem, you can use FlyTreeView.GetCheckedNode(radiouGroup) method in order to get checked node for required radio group.
Or you can create a helper Page class collection field where you can store checked nodes collected during LoadPostData treeview events. And use it in Page_Load or later.