Jetpack is a plugin that provides security, performance, marketing, and design tools.
Both plugins work fine together. There is just one particular scenario where you might observe something not working as expected. And that is the author name for guest and/or co-authored posts displayed on subscription emails.
So, if you don’t use the Subscription emails feature that Jetpack provides, there’s nothing you have to worry about and you can skip reading any further. The same applies if you don’t use the guest posting or co-authoring features that Molongui Authorship provides you.
Jetpack sends subscription e-mails from WordPress.com servers —not from your own installation. To build those e-mails, Jetpack gets the data from your site without taking WordPress core filters into account, thus ignoring author configuration you set on that post. This is a bug Automattic —Jetpack’s developer— is already aware of. Let’s hope they consider fixing it soon.