How do I sync podcasts added in the iPhone's Podcasts app to iTunes on OS X?
I think for this to work, you need to enable iCloud syncing for podcasts between your devices. The setting you refer to above only applies when you sync your phone from iTunes, either via USB or Wi-Fi. I could be wrong, but as far as I know it only syncs podcasts from iTunes to your phone, not the other way around.

Also, make sure there is enough space on your phone for all those podcasts.