Is it possible to control the PowerCable MQTT 101x output using a mobile app?

Yes, in several ways.

We released new “NETIO Mobile 2” app for Android, which supports this product. For iOS mobile devices, NETIO mobile app upgrade is not available yet.

However, thanks to the open API, third-party MQTT mobile apps can be used, too. For details, see AN40: Getting started with PowerCable MQTT-flex via HiveMQ MQTT broker to mobile App