Indeed Enpass is an offline password manager and saves your data locally on your device and in any case, we do not (and we can not) access any of your data.
But yes, Enpass does connect to the internet with the sole purpose to give best user experience. If you have seen a network activity for Enpass, it could be due to any of following reasons:
Why do we do so? Being offline in nature and having no information about our users (except those who have signed for our Beta program or newsletter) makes it impossible for us to reach you. In case if there is some significant news (maybe security related like FREAK Flaw) to share, which might require immediate action by you. That is where this becomes the only medium from where Enpass can pull any such information.
You can disable the participation in analytics from Enpass Advanced settings.