You should purge content on Akami CDN after Sync.
This documentation should work the same for eSync Strategies because we have CMS Extension described in the following link.
You should use an extension to call the Akamai APIs to purge cache information.
The following video links shows you how to build an integration into Akami via a CMS extension (plugin) for forward caching capabilities:
Also, there is LibraryStrategy code located here.