Not by default, no. Subtasks are only attached to a project if you explicitly add them to the project.
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@Phil_Seeman any thoughts on that?
It’s not obvious, but you can use the shortcut [tab]+[p] to ad another project.
I’m referring to this Jan…,
Well, you would need some kind of trigger.
It’s a bit hard to advise you without understanding the place of this in your process, and the why behind the request.
If you’d like we can set up a call to talk it over. DM me if you’d like that. This one is on the house. 
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love to do that. 
check DM
I don’t know of a way to automate that in native Asana.
You could do it using our Flowsana integration; what you would do is create “Bug reported by” as a text custom field, then create this rule:
Note that this takes advantage of our Variable Substitution capability.