I was having this issue. None of the above methods had helped stop the phone from announcing which desktop I'm currently on when I swipe over "Page 4 of 7", "Page 5 of 7". My Talkback service is turned off, as well as Driving Mode. Likewise, I've tried disabling all kinds of text-to-speech options in an attempt to solve it, but no luck.
The only special app that I could think of that could be affecting this is my lockscreen widget app, called
NiLS. It just offers a widget for your lock screen or home screen that shows any incoming notifications in a nice, minimalist text, which I really like for my lockscreen. However, the widget requires a service to run on the phone, which shouldn't cause any issues, but apparently this is a bug in Samsung Galaxy S3 phones? I disabled the NiLS notification service, and the voice stopped notifying me of my homescreen page.
For anyone else that has this problem and, like me and many others, you've searched all over the internet for a solution, it appears that this is a bug with Samsung Galaxy S3 phones using some apps that install a service in the Accessibility area of the Settings of the phone. I'm no Android expert, but my gut tells me this can't be fixed without a bug update/patch for Android or possibly the apps themselves, but my phone is fully updated via Settings->About Device->Software update. For now, I think you'll have to disable the service(s) those apps are using and the voice notifications
should stop. As for which app services cause the issue and which don't, I have no idea. There are a few listed above by other users that seem to also cause the issue, as well as the one I was using, NiLS.
My phone:
T-Mobile Samsung Galaxy S3 LTE (stock, no root)
model: SGH-T999L
Android: 4.1.2
Hope this helps to everyone. If you can, like this post so others find it easier.