Unfortunately, the seeing I provided is a global setting. There isn't a setting for individual site servers at this time. You may submit an enhancement request, and that will allow Product Management & Development to see what it is the customers desire.
As for Update Configuration; that is the Site Server Agent that will request any new Patch packages. This setting is managed on the Console > Settings > Agents/Plug-ins > Symantec Management Agent > Settings > Symantec Management Agent Settings - Targeted; select the 'All Site Servers' in the Policy Name pane, and on the General Tab under 'Download new configuration every:' and that will be when the Site Server will download packages.
Another thing to keep in mind; on the Windows Patch Remediation Settings > Policy and Package Settings tab; under Package Distributions, the 'Assign package to:' setting controls which Site Servers will get Patch Packages. There are 4 options, and the one that is not self-explanatory is the 'Package Servers automatically with manual prestaging'
The setting for 'Package Servers automatically with manual prestaging' configuration will only replicate Patch Packages to Site Servers if the Clients they manage request that package from that Site Server, and that request is sent to the SMP Server to replicate the package out to the Site Server for deployment. This setting has been confusing in the past for many and I wanted to ensure you were aware of it as you are configuring the environment.
This is covered in the configuration KM: HOWTO56242 - Section 7, for the 'best practice' setting is 'All Package Servers' as that will get the packages out there and ready for clients, for I have seen environmental communications issues that lose that 'request for package' from the clients, or from the Site Server and the package is never replicated with the 'Package Servers automatically with manual prestaging' setting in place.
Let me know if you have any further questions and I will be happy to help.
Thank you,
Joshua