iOS supports two ways of fetching new emails while the email app is not active: One is via push notifications and the other via reqular background fetches. While push notifications are sent by a cloud service and can been received at anytime, background fetches are scheduled by the operating system in regular intervals that depend on many parameters.
Many other email apps on iOS use the push notification approach. This requires a permanent connection from their servers to your email provider. To do that, they send themselves login credentials to access your account from their servers. To us this raises quite a few privacy and security concerns, especially if the user isn't made aware of this.
We are currently evaluating how to implement this approach in a secure and privacy-aware way.
For now Unibox uses background fetches that are initiated by the operating system. For those to kick in you'll need to use the app regularly for two to three days. After this training period notifications for new emails should start to appear in intervals between 15 and 30 minutes, comparable to the native Apple Mail client.
If notifications still don't work after a few days of regular use, please check the background settings for Unibox in the system settings or contact us.