I don’t actually see Jetpack sharing on the post you linked to. I see another sharing plugin is active, which I think is powering these buttons.
We can rule out a theme conflict by temporarily changing your site’s theme to a default theme (such as Twenty Fifteen) and trying again. If you’re willing to do that, give it a shot and let me know.
You can also check whether any other plugins on your site may have a conflict. Please check our Known Issues list here:
https://jetpack.me/support/getting-started-with-jetpack/troubleshooting-tips/
Depending on the outcomes of the theme switch you can also try to deactivate all plugins on your site, and see if that resolves the issue. If it does, then activate them one at a time to determine which is causing the conflict.
Hope this helps us get to the bottom of this issue.
Jesse