Hi @Adam_Dudley and thank you for reaching out and for sharing the screencast. It is very helpful to understand the issue.
This is actually not a Bug rather the expected behaviour. Let me give you some context here to explain you this behaviour.
As it stands, subtasks do not automatically inherit the project from their parent tasks. To do so, you will need to manually add the subtask to a project (you can learn more about it in the following Guide article. One of the ways to do it, is to drag and drop the subtask to any section of the Project (as you have done).
Once you do that, the subtask will appear in your project’s task list, Project Calendar and Project Timeline function like independent tasks with all the same fields as a parent task, with the difference that they are also embedded within a parent task. Reason why you are seen it in both nested in the Parent Task and under the Section where it belongs.
When viewing a subtask’s details, you can identify the parent task’s name above the subtask’s name and the project and section where is nested.
You can read more about subtasks in this handy article: https://asana.com/guide/help/tasks/subtasks
I’m sorry for the confusion and I hope this helps! But please, let me know if you have any follow-up question! I’ll be more than happy to help!