They spawn roughly one essence crystal an hour, to the max of 6, and they do not start the spawn timer til the first time you log in after the event starts. So you will not have your first one to collect til at least an hour after the first time logging in with the event active.
I logged into the game right after it started this morning and then went to bed and I had my usual 6 to collect when I got up and loaded the game again.