Your understanding seems correct.
In fact ALE server will agregate all Wifi data (RSSI, location, geofence_notify, application ...) and expose these to third party (via 0MQ message bus and rest API).
So in your case Purple will be the third party which will connect to ALE to get data for analysis.
And you don't even need AirWave for ALE to work. There is a node (calibration mode) in which you put the maps directly on ALE and then you calibrate with your android smartphone.
Hope this helps,
Fabien