Summary
Changing the deal owner doesn't change the deal task assignee.
Resolution
To assign both a deal and the associated deal tasks, delete the account user assigned to the deal. Doing so will give the option to choose a single account user to transfer the deal and tasks to.
Cause
This is expected behavior. When attempting to manually change the deal owner, or create an automation that changes the deal owner, any deal tasks associated will remain assigned to the previous deal owner.