Hi @Cindy_Cheng, welcome to the Asana Community Forum! 
and thanks for taking the time to share your feedback with us!
Subtasks do not inherit the project or assignee from their parent tasks right now. You can affiliate subtasks with projects by going into the subtask details and using “Tab+P” to open the project field or by going to the upper right drop-down and selecting “Add to Project.”
I also suggest you to add your vote to this request: Allow to automatically add subtasks to project
I’ll make sure to keep you posted once I have any updates about this feature!