By what process is a third party device configured to connect to the WiFi network I'm wanting to understand what is happening when a device needs configuring with WiFi credentials, but no other communication is apparent.

For example, with the Broadlink RM Mini3 WiFi IR Blaster it's a rather simple process: download and run the required app from the Play store, enter the WiFi details (SSID, Password), turn on the device and click connect within the app. A few seconds later, the device has been configured to run on the relevant network.

By what process is such a device configured when there appears no bluetooth connection etc. that would facilitate the initial connection.
It's different for different devices. Some use Bluetooth or NFC, but as you've observed that's not what's happening in your case. The most common alternative is that the device you're configuring can itself act as a Wi-Fi access point (AP): it creates its own Wi-Fi network. Your phone connects to the device's Wi-Fi network and sends it the connection details for the network you actually want, possibly via an HTTP request to a simple web server running on the device. After that, the device shuts down its Wi-Fi AP and connects to the Wi-Fi network you configured.

If there's a network problem, the device should start its own AP again to let you connect and give it some new connection details.