Stormed Off

One rare spawn at the very start of an event popping, and then seem to be randomly every 30-50 minutes or so after that.
This is the type of Storm event needed for each of the rares to spawn:

Elemental Air (Thunderstorm)
After a hotfix they all drop Formula: Illusion: Primal Air
[npc=193684]
[npc=193674]
[npc=193653]
[npc=193647]

Elemental Earth (Sandstorm)
After a hotfix they all drop Formula: Illusion: Primal Earth
[npc=193652]
[npc=193680]
[npc=193644]
[npc=193654]

Elemental Fire (Firestorm)
After a hotfix they all drop Formula: Illusion: Primal Fire
[npc=193686]
[npc=193675]
[npc=193650]
[npc=193648]

Elemental Water (Snowstorm)
After a hotfix they all drop Formula: Illusion: Primal Frost
[npc=193655]
[npc=193682]
[npc=193679]
[npc=193645]

Your UI will display "XYZ has appeared!" in the middle of your screen, and in your chat log when the mob spawns.
The mob is instantly attackable (no warmup period).

So if you're camping waiting for the mob - stay somewhat central and just keep an eye out for that shout, then quickly find and tap the mob.

To add to the information given in the first comment.

I tried waiting for a rare after killing the first by myself on my own shard for more than an hour and it didnt spawn. Unsure why.

Since then, i keep my shard and make a raid group. Ive killed the first rare in a storm and waited around 35 minutes from time of death each time for a respawn. That seemed to be the appropriate amount of time when i tested it one night.