There is a report "Package Status by Package Server".
You can use it to see what is a state of appropriate package on required Package Server.
Note:
In hierarchy, this information will be updated on Parent SMP server as soon as appropriate Child SMP server will perform replication UP to Parent NS to populate all latest information (Speed of latest data population from all Child SMP Servers to Parent SMP, depends on what schedule is set for "Differential replication" on each Child NS).
If you see that "Replication down" job is successfuly completed from Parent NS to Child NS, you can check this, using "Replication Jobs management" page on Parent SMP Server. If status is green, then replication job is successfuly completed. If it has another color, then you can open detailed information about this job and check results.
If you are using "Software Management Solution" and want to replicate down a new "Managed Delivery" policy which has a new packages, then you can use an option "Emergency Policy Update" on Parent SMP Server = After that this MD policy with specified software packages will immediately replicate to all known Child SMP Servers.
Thanks,
IP.