For object types to appear under Devices in the More Service Sync app, the object type must be configured for this.
Open Settings → Asset → Object types
It shows all accessible object types that can be configured for the sync service and Asset module.
The icon on the right gives an indication of whether an object type is configured or not
To configure a object type for sync, press the desired object type and you will get the following dialog
By turning on "Configure for sync and asset" and then clicking Save and close, the object type will automatically be configured for sync to Asset module.