Unfortunately this is not possible. I've struggled with this from the start and while you can spawn as many tickets as you want from a task it will not populate information from the Parent. The only way I got around this was to treat a new employee ticket as an approval request. When a new ticket is entered it creates and sends an approval request to all the included areas and they know to respond with Approved once their part is complete. This way I have all the information on one ticket instead of several for the same new employee. Not ideal but at least it works.
We also have struggled with this. I have created approval processes for each incoming and outgoing employee as well as change of status. The issues include that things must go in order of the approval process which is sometimes good and sometimes not. There is not a way I have found to enable easy way of changing of the ticket status to resolved or closed when the approval process completes.
We also bumped into this short coming. The work around we put into place was to create a custom field that is a checklist of action items that need done for each request type. This custom field is a Multiple Choice type so that as each item is completed the 'choice' can me checked off within the ticket. The single ticket remains open and is passed between techs that complete each step.
i.e. Email; Access Card; Orientation; Payroll
Item(s) within the multiple choice checklist can also be detected with an Action Rule, so that you can detect when all or parts of the checklist is complete. Notifications and/or tech reassignments, etc can be made on the ticket this way.
It is less than ideal but has been working for us.