Indeed Enpass is an offline password manager and saves your data locally in your device and in any case we do not (and we can not) access any of your personal data.
But yes, Enpass does connect to 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 we do so? Being offline in nature and having no information of our users (except those who have signed for our Beta program or newsletter) makes it impossible for us to reach you, in case there is some crucial news (may be security related like FREAK Flaw) to share, which might requires for an 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.