You can block Office 2013 Click-To-Run (CTR) from automatically updating to 2016 through a policy (or registry if you're not in a domain).
If you have the Office 2013 Group Policy templates installed on your domain controller, you can use them to set a policy to disable automatic updating.
You can find the setting at:
Computer Configuration → Administrative Templates → Microsoft Office 2013 (Machine) → Updates
Set Enable Automatic Upgrade to Disabled.
You can also disable the upgrade by manually adjusting the registry.
In regedit, navigate to the key:
Create a registry value: