It is my understanding that although an available update may download automatically, especially if connected to Wi-Fi, you still have to initiate the actual installation of the update and therefore, only the 'data' that was actually backed up to iCloud will be restored.
In your initial post, you basically stated that you made a backup on a device containing iOS 6.1.3 and want to restore it to a jailbroken device running iOS 6.1.2 using iTunes. Well, according to THIS (The second line under Resolution), you cannot restore a backup from a newer version of iOS to a device using an older version of iOS. I can only assume it's whether the device is jailbroken or not.
I had a backup on 6.1.2 and got a new phone still on 6.1.2. Icloud wouldnt allow me to backup via my phone. When I went onto itunes on my pc it allowed me to restore from my computers backup. Didnt say anything about firmware update and had me scared. Still on 6.1.2 So happy