For those that don't know, Primal Summoning has been a concept that Yoshida would have liked to add to the game if they could work out a perfect system for them. It was basically an FC type content where you and your FC mates would work on summoning a Primal that other players would hunt down and kill. It sounded a lot like special boss fates like Odin and Ixion but these were summoned from players and then they roamed the open world.
The reason I made Ixion in bold is because anyone that tried fighting him for the first few months of Stormblood launch will know that XIV is not a game designed for an open world focus. Unless the devs put in a lot of money on improving things, any kind of big important open world content is just going to be a really painful experience with congestion in areas and mass amounts of disconnects and lag.
If Eureka is anything like Diadem, then it will most likely be an instance for a max of 72 players. This keeps the open world feel but it doesn't have all the bad stuff to it like Ixion had. The only downside is that Diadem became very quiet after the first few weeks so the open world feeling was lost since most people did the basics and then left or AFKed.
Here are some ideas I have for how to prevent this type of content being dead after a first few weeks like Diadem was.
Have some kind of panel that players can check if a "Primal" is active in Eureka from the main game. Like say in Mor Dhona, Idyshire and FC Houses. When a "Primal" is active, a message goes out to all players that the panel has been updated, similarly to the "XYZ amount of parties are recruiting that match your description" that we get every few minutes (Players should be able to turn this off from the chat menu if they don't want to see the message). Anyone who enters the instance for the next hour since the message pops up will be able to fight this "Primal" in their Eureka instance.
Also to make Primal Summoning more fun, I thought that it could encourage people to run the primals they want to summon with level sync and minimum item level. Say for example that to summon a primal we need to have some residual primal energy on us from killing the primal so many times. An undersized party would give a very restricted amount, a normal level sync would give a decent amount and minimum item level kill of the primal would give a large amount.
Edit: Also another way to get a big boost to summon your own primal could be to kill other peoples Primals in Eureka. Having this ontop of what ever reward you want to give people for doing Eureka could be a nice way to keeping the content somewhat active.
Credit for this idea came from this reddit thread.