Only ch1 has a counter. For me at least, it counts down nicely till around the two minute mark, then anywhere from 2m to 1m:10s, it just goes away sometimes not coming back till it's over.
Yeah, there's no timer displayed but it seems to be on roughly the same timer as ch1. You can check the status of the event by clicking on the EoJ vendor in the zone. If the top players can be displayed, the event is down. Otherwise, it is still going.
You can make your timer reappear by doing one of a couple of things:
1. You can complete a quest that awards points.
2. You can zone into the next chunk and it will bring it back up for you.
This, incidentally, is the way that you do events on ch2 in Rorazan as well. In Rorazan, the events are on a timer that starts the event on the 10th, 30th, and 50th minute of the hour and I would imagine that the events in Chrysalia run on a similar, if not the same, timer.
I haven't really spent much time doing the new events with the stats having been nerfed so horribly. To be honest, I haven't logged in to do anything but check my traders since the second day of the new expansion largely because of this. I guess that's the result they were looking for, though.