I've tried changing my profile picture according to How do I change my profile picture, or avatar? , and it worked fine for all sites. However, on my network profile, I still see picture from my associated Google account. How do I change this one?
If you don't have a profile there, it automatically syncs to your oldest profile on its own schedule irrespective of clicking on the button to copy to all sites. I manually triggered the sync for you and it's updated now.
If you ever do create a profile on stackexchange.com, you'll have to copy it over manually.