Does that application support AppConfig standard Managed Configurations? You're only going to be able to configure the app through SOTI if it provides a mechanism for configuration. This traditionally means an external configuration file that the app can read from but can mean a Managed Configuration through more modern approaches like you've mentioned above, but the app itself has to be coded in order to support them. There are other options that some apps may exposed like Intent driven configuration but those are significantly less common. If the app does support Intent driven configuration then that can be administered via SOTI scripts. At the end of the day SOTI gives you a lot of options but the app itself needs to support the configuration mechanism that you intend to use. 

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I just did a quick search and it doesn't appear that the application in question supports Managed Configurations due to how it's listed in the Play Store:

Normally you would see something more along these lines:

I'm building an inventory application with the intent of using a Managed Configuration.  I have all the documentation I need for the app.  What I'm missing is what we need to do with SOTI to manage the Managed Configuration.  I've looked through the help guide and can't find anything about it.

Two questions:

Where in SOTI MobiControl can we set up deployment rules for groups of devices to provide an initial configuration at the time of app installation and after installation?

Does this work with the device agent or do we need to have the enterprise agent on the devices?

AppConfig compliant configuration mechanism is supported for Android Enterprise devices.  Different parameters are configured in the Advanced menu of the Managed Google Play Store app defined in any Android app-catalog rule.