Spoiler Alert! We have hidden this information so that you have the choice to try it on your own, or have the advantage of knowing how the sausage is made...
To get Zalkenrys to appear, run around the plateau and kill many machines. At some point you will see a broadcast message that Zalkenrys has been activated.
Killing Zalkenrys will update the quest for all members of the party.
In all other zones they do not reward XP, TP or Gold, only Public Event Points. In all other aspects they are the same as a Daily Quest (except for the infinitely repeatable part and the rewards). Public Event Points contribute towards the completion of Regional Quest objectives, which in turn rewards a number of Energy of Justice commensurate with your amount of participation in the Regional event.