Hi Lindsey,

Completion is per user, so what you are seeing is expected. Completion cannot be used to share a task list unfortunately.
As for how best to achieve this at present we don't have functionality to facilitate this easily.
I am aware of third party plugins such as the Checklist activity that may achieve what you want.

Alternatively if all of the staff responsible for on-boarding a new user are also trainers then you could use a label or page activity to maintain a list and require each staff member to update it manually after completing an item. They would need to edit the activity and change the state of the item.

Kind regards
Sam Hemelryk