By default, additional managers won't have access to the user's contacts tab.
If you want them to have it, you can edit their access rights by following the steps below:
Click Access Button
then click Employee.
Click Overview, then click Edit Access Rights.
Click on Contacts and set to Update.
Click Save.
📌Note: There is no view-only option for this, therefore users with edit access rights for contacts would be able to update this information.