I believe that the problem is the posts themselves are being published by the Cron Job, so the post author isn't the one actually publishing it.
As such, it doesn't have access to the post author's Publicize connections.
This is a bit of a security reason, as if Editor B were to write something and switch its author to Author A (who has their social accounts linked via Publicize) they would potentially be able to hijack Author A's social media accounts.
I'd like to find a better way to test for 'last modification' so we can, but at the moment that's why. If the publicize connection was shared with anyone on the blog, then I believe it would work off of the cron schedule. (I've not actually confirmed, but I believe that to be the case from thinking it through)