This information can be found in the logs of your SUPPRESS account.  There are several different types of logs available in SUPPRESS, but a common one to review in this case is the Affiliate logs - this will show you the activity of a specific Affiliate.

To view an Affiliate's log activity, follow the steps here: How do I View the Activity of a Affiliate?

then scroll down to the bottom of the page.  

An Affiliate has successfully downloaded a Suppression List/Opt-Out List when you see the following two log entries.

- prepared a download: will let you know the Affiliate entered accessed the Campaign and triggered the action to get the Suppression List ready.

- downloaded the suppression file: will let you know the Affiliate has downloaded the file from our servers

If you have further question, please contact us at: support@optizmo.com