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).

Group Policy

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.

Registry

You can also disable the upgrade by manually adjusting the registry.

In regedit, navigate to the key:

HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\office\15.0\common\officeupdate

Create a registry value:

• Type: DWORD
• Name: enableautomaticupgrade
• Value: 0