In this instance if you don’t want it showing in the child project my suggestion would be to complete the subtasks in the template, then when you duplicate the parent task change the status of the subtasks to incomplete. Also, make sure that the child project is set to only show incomplete tasks.
I know this isn’t the best, unfortunately, in Asana, templates of any form are not the most advanced features.
These are popular requests, and I suggest voting on these two product requests.
https://forum.asana.com/t/custom-task-templates/4676
https://forum.asana.com/t/template-assigned-tasks-show-up-in-my-tasks-automatically/4125