If you created the same scheduled job on both replicas, and are not doing the right backup config, you might be creating a mess with your backup chain.
The fact that the backups are not failing, means probably the FULL backups are happening with the COPY_ONLY parameter, otherwise the backup would fail on the Secondary (Read Only) replica.
AlwaysON allows to control where your Automated backups happen, as per the Backup Preferences set on the AG. The Automated backup jobs should check if they are running on the preferred backup replica. If they aren't, they will not run there (by design).
You indicated that your backups effectively run on both replicas. If your Log backups are also running that way, I wish you good luck trying to piece the backup chain together when trying to do a Point in Time restore (by the way, have you tried restoring a database, with t-logs ?).
I'd suggest reading up on backups on AlwaysON. A good resource to start is Configure backups on secondary replicas of an Always On availability group, but you will find many other good resources on the 'net.
What peaked my attention on your article is that both of your replicas were doing the backup, which means your backup setup is not configured properly. backups should only be running from the Preferred Replica, not both servers.
For better assistance in answering your questions, click here[/url]