On the SMP server, you have set up the "Windows Patch Remediation Settings> Packages tab" option to "Package Server (PS) automatically with manual pre-staging".
You are expecting a package to be only downloaded to SMP Site and not to be distributed to any PS (outside this SITE) as there would be no clients requiring or requesting this package (no policies).
But this package gets assigned to all Package Servers.
Seems to be reproducible in a simple environment, even with a new Software package (no policy) created being assigned right away to 2nd Site (with no clients)
ISSUE REPRODUCTION
On the SMP server - with Remediation settings set for package "automatic assignment with manual prestaging" download any non-used Bulletin, without creating a policy of SWD delivery. Package by default assigned to all Sites.
The expectation is that this package after being downloaded to the SMP server will be then assigned only to the SMP Site Package server, and would only be sent to remote Site Package Servers if there are clients available which would require this package (based on policy)
COMMENTS
Initial idea is to get the product to work the way that remote Site Package Servers should not get packages clients would never require. For example, you might have a site with Server OS only, and another site with Client OS - so the expectation that Server Site PS would only have Server Bulletins and Client Site would have Client bulletins. As a current state - both sites have both types of packages (consuming more disk space than required)
ITMS 8.5, 8.6, 8.7
Default package assignments for Patch Management and Software Management Solution are set in this way (By default "Site" with remote Package Server isn't checked so any newly downloaded Patch update package or imported Software Package will not be automatically downloaded by remote PS)
Verified that already downloaded Patch Update package is now distributed in Patch policy and the client received this policy and tried to download this patch update package, only after this remote Package Server on policy refresh will download this Patch update package and share it for the client.
Same behavior for imported new Software packages.
We have done some tests for Patch Update packages download without distributing in patch policy and SW release import without the creation of Quick Delivery task or MD policy == Remote Package Server doesn't automatically download new packages and will download only if there will be policy created and the agent will ask for such packages downloading or quick delivery task executing on the client-side, then PS will download these packages and offer to download it for clients.
Found a case when a client not from PS subnet is targeted to Patch policy, but if this client is "Manually Assigned" to this Package Server on Site Server Management page, then PS will download these packages for this client, even if the client is not in the same subnet with Package Server.
But this manual assignment doesn't cause packages to download by Package Server if the Patch package just downloaded without Patch policy creation or SW package just imported and included in MD policy.
If on PS selection, for package distribution you have selected PS/Site - the package will be sent there regardless of the Drop-Down menu setting - Manual Pre-staging.
A manual pre-staging setting applies later if a client on this Site will request this package - only then the package will be force-downloaded to Package Server.