Issue links in Jira are a helpful tool to keep track of changes throughout different issues.
In the following use case assignee that is added to the current issue will be copied to all sub-tasks.
Add the Update linked issue or sub-task post function to the desired transition or create a new transition.
Click on Add field.
Choose Assignee
Choose Copy field value form current issue
Click on Add
Update the following filters according to your needs.
Choose Sub-task
Update linked issue or sub-task