It might be that the eSign document was added after the creation of the new hire, therefore new documents will not be automatically added but the customer would need to manually have the eSign request sent to them via the Action button.
Another possibility of why the esign request was not created for the new hire, is that if the eSign template contains required fields that were empty on the EE profile at creation time.
Note: all fields must be there on new hire wizard, not on employee onboarding step.