Hey Will, I may be wrong here but, Considering I have the messenger installed at my site and working without a OneSignal account, how could OneSignal be storing my website's messages?

From my understanding, Jot Messenger uses Jot Server and not OneSignal to provide messenger services. OneSignal would just be used for the 'notification push' to your browser and/or mobile device. Although they may store the notification push, I would not think that they are storing 'complete' conversations from the messenger or any other content on your site.

That would be considered a 'back door' hack to steal website data. I don't think that is what's happening here. Can you provide where you found that OneSignal stores all of your conversations used by Jot Messenger so I can see for my self?