Yes, the device and the app need to be in the same release channel. If you install an app in the Alpha channel, it will only be installed on devices in the Alpha channel; it will not appear on devices in the Beta or Production channels.
In addition, when you replace an app, you replace it on any device that has the app installed in the same release channel. For instance, if you replace an app in the Alpha release channel, it will be updated on any other device that has that app installed in the Alpha channel. The app will not be updated on devices that have it installed in the Beta or Prod channels.