For the most part the Home app works perfectly well with Eve accessories. However, Home has different features than the Eve app.
For all of the details, please see the Eve Blog:
A brief summary of those details is below.
Types of information that the Home app cannot access
HomeKit uses various types of information (also know as characteristics).
Some custom types used by Eve are not predefined by HomeKit, and therefore will not show up in Apple's Home app:
• Eve Energy - Energy Consumption, Historical Data
• Eve Thermo - Offset Temperature, Historical Data
• Eve Weather - Barometric Pressure, Historical Data
For those types of information, the Eve app needs to be used.
HomeKit and Siri in iOS 10
Siri in iOS 10 has been extended, and it can now answer more questions about Eve accessories in English.
• Eve Door & Window - Contact Sensor State ("Is my Kitchen window open?")
• Eve Room - Air Quality ("What's the Air Quality in my Living Room?")
Custom types used by Eve accessories cannot be accessed by Siri. For example, you can't ask Siri about Barometric Pressure.
Home app and Rules with Conditions
The Eve app allows you to establish many rules with conditions, so that the state of one HomeKit accessory can affect other accessories.
Apple's Home currently lacks support for rules with conditions.
Therefore, if you want to establish rules with conditions for your Eve accessories, use the Eve app.
Changes has Apple Made to Apple TV and HomeKit
Apple has made some important changes to how you can access HomeKit devices from outside your home.
You can set up your iPad or Apple TV (4th generation) as a home hub to automate and remotely control your HomeKit accessories from your iOS device. The device you set up as a home hub must remain in your home, connected to your home Wi-Fi network, and powered on.
Please note that the Apple TV (3rd generation) is no longer supported. This is due to changes that Apple has made, and not due to any HomeKit accessory vendor like Elgato.
Also, be aware that to set up your Apple TV (4th generation) as a HomeKit hub, you will need to turn on two-factor authentication for your Apple ID.
Please see this article for all of the details, including setup instructions: