But I do not know how they managed to set up a purse so that it automatically sends eth
A simple script receiving PUSH notifications from one of the public APIs... that waits for notification and immediately broadcasts a message transferring the coins out. It's also possible to do if running your own full node and some scripting "magic" 
I believe the user "amaclin" did something similar a while back with BTC and CounterParty tokens. From memory he published the private keys of an empty BTC address with a number of XCP tokens attached to it... I remember looking at it and thinking "Devious!"...
However, I can't seem to find the thread/post now