Thanks for posting the official translation on that, Bayohne, but I've to agree with Reinheart here. The randomness of these events is quite uncomfortable and requires too much time or luck for the casual adventurer to catch.

Although I really appreciated the reward of the secret area in Mistbeard Cove, The Whale's Cape, and changed my original Topic in a more positive note, I still believe this randomness won't do much good for casual adventurers with not much free time.

I spent many days trying to figure out a pattern and in the end didn't find out much, probably because I'm not smart enough (or there's no pattern at all).

Like I said, I did both of these events and enjoyed them, but, as a casual, my tactics was to either craft in the same spot or go to Eorzea every hour, taking airships/teleporting to other city-states. This, of course, only in late afternoon or evening/night.
Not the best of comfort for me, as I like to craft in different places, nor for another adventurer that could stay in Eorzea even less than me, like from 21.00 to 00.00.

By the way, the name of the cultists is “The Lambs of Dalamud”, not “The Lamb of Dalamut”... Sorry for the correction, vine-man! And I hope you community reps noticed this other similar Topic here.
Even if that matter wasn't brought up in the Japanese board, I wish it'd be taken into consideration, as well as gradually change the occurrence of these limited-time, story-related events. Thanks if you forwarded it to the devs.