Current Behaviour
New sub-tasks on JIRA Agile inherit the Fix Version/s field from the parent issue (see here).

Current Workaround
Remove the project from the projects 'Enabled for JIRA Agile' in the JIRA Agile configuration.

There is currently no way to disable fix version inheritance for Sub-tasks for JIRA Agile enabled projects.
It would be great to have the possibility of configuring this behaviour to disable fix version inheritance (e.g. a checkbox on the JAG configuration screen).