This is due to the item being added to a board which is only visible to members of the team.
You have two choices here:
Add the person in question to the team
Make the board publicly editable - in which case all employees can add/edit/delete items in this board
The first option can be accomplished by:
Navigate to the Teams tab, select the relevant team and click on "Configure Team"
Navigate to the People tab, add the employee to the team and Save.
You can now allocate items within that team to the employee
The second option can be accomplished by:
Navigate to Configure Team and select the Work tab:
If the Board is private then select the Edit button and change the permissions. Save & Close once done.
What happens next?
Tickets can be allocated to any employee, whether they are on the team or not.