Eve Door & Window is designed to log open/close events for doors and windows in your home, and stores the events on the device. You can check on the state of Eve Door and Window with your iPhone while you are in Bluetooth range. To determine whether your door/window is open or closed while you are out of Bluetooth range, you need to add an Apple TV (4th generation or newer) that acts as a Bluetooth bridge to your HomeKit setup.
To enable HomeKit notifications for open/close events, you will need the latest version of the Eve app as well as iOS 10.2 or later. Eve Door and Window also needs to have the latest firmware installed.
Follow the steps described here: https://eve.help.elgato.com/customer/portal/articles/2150038 to enable HomeKit notifications, and check out https://eve.help.elgato.com/customer/en/portal/articles/1988890 to learn more about monitoring and controlling Eve accessories away from home.