@celestialpainter When you answer your clients through the mobile app doesn’t mean they need to have it as well. The mobile app is your tool the do actions on the go without having to be near a computer, e.g answer chat messages. if you answer from the mobile app it will go to your clients email, same as happens in the Inbox on desktop.
If you are managing multiple sites what I suggest is to add yourself as a contributor with the same email in all of them and this way you will be able to see all of them in the app when you login with this account and you will be able to get notification on all sites and answer them immediately.
Let me know if that make sense to you.