This means that nobody but you can access your data, and neither Apple nor Elgato know what devices you own and what status they have.
Therefore, as no server or service has access to this information, Push Notifications are not supported.
However, two different types of Notifications from Eve Accessories are supported:
1) Triggers and Conditions, used for Eve accessories and other HomeKit accessories to communicate
2) Special Home Notifications that appear throughout iOS, including on the device lock screen and/or home screen.
Triggers and Conditions
HomeKit accessories use Triggers and Conditions, which are different from Push Notifications.
HomeKit accessories such as Eve Door & Window can automatically trigger a HomeKit scene when certain conditions are met. For example, to turn on your lamps when your door is opened.
Eve supports all HomeKit-based triggers (location, time, accessory) and conditions.
See this article for more details:
Eve 1.5 — Event-Based Triggers and Conditions
Home Notifications - Lock Screen and Home Screen
In addition, Eve 2.5.1 and iOS 10.2 support Home Notifications for Eve Door & Window, and Eve Motion.
See this article for more details:
Finally – Notifications
Those special notifications will appear throughout iOS, including on the device lock screen and/or home screen. That means you will automatically be notified of value changes, namely when a door or window is opened or closed, or movement is detected.
Your iOS device does not query the HomeKit-enabled accessory about value changes. Instead, the accessory delivers values changes to your iOS device. Before iOS 10.2, you could only see value changes in the Eve or Home app, where they were automatically updated. Now, with iOS 10.2, you’ll see an additional notification.
Enabling Home Notifications for iOS
To receive notifications from Eve Door & Window and Eve Motion, you need to activate Home Notifications in the Apple Home app, as only Apple Home permits necessary access.
1) In Home, tap and hold on a tile representing Eve Door & Window or Eve Motion
2) In the following screen tap Details
3) Scroll all the way down, and select Status and Notifications
4) Activate Allow Notifications, or deactivate it if you don’t want to receive notifications
Home Notifications for Eve Motion will be turned on by default, as soon as you install iOS 10.2.
Home Notifications for Eve Door & Window will be turned turned off by default, as soon as you install iOS 10.2.
To set where and how notifications are displayed on your iOS device, go to iOS Settings > Notifications > Home
Home Notifications and Guests
Guests of your home will receive Home Notifications via their iOS devices
More Information about Home Notifications
There are no push servers associated with Apple, Elgato or another party. Communication occurs via direct end-to-end encryption between an Eve accessory and your iOS device/ Apple TV 4. We at Elgato expect that notifications for our other accessories will be enabled in the near future.
Notifications will still work if you do not have a home hub (Apple TV 4 or iPad with iOS 10 in home hub mode). However, they will only work locally, and if your HomeKit-enabled accessories are in Bluetooth range of your iOS device. Although this setup does offer some benefits, it’s not entirely practical, because in most cases you’ll want to be notified while you’re on the road. As such, to receive notifications remotely, we recommend that you set up an Apple TV 4 in your home.