@ENelson 5407eb1 ahschools
Interesting workflow - It got me testing a few things out.
I encountered the same issue where the subticket would be assigned to "system services" when the rule was triggered. I suspect this happens because the rule is essentially creating that subticket. Unfortunately, there is no option in the rule to add the additional action of "Assign to the submitter."
I would suggest, submitting a support ticket to see if this is intended with the rule and ticket template. If so, I would submit an enhancement request in our Idea exchange.
I know it is not exactly what you are looking for, but I did test it without having the rule trigger the subticket. I created two ticket templates; one is the parent ticket, and the other is the subticket. When submitting the ticket using the parent ticket template it will assign the submitters as the agent of the subticket. Create the video below to explain it better