My theory is that after the six days are up there will be crystal bloom npcs that you can take on missions. I assume that they'll bring some new feature or mechanic. It also looks like, depending on the amount of participation in the six day event, you will be able to get some sort of bonus rewards from a new vendor NPC that will appear with the crystal bloom contingent. So, I think you just need to do enough missions to earn five of the crystal bloom support crystals and spend them at the vendors. It's not clear to me whether obtaining and spending more crystals will give you higher tiers of rewards, or if those come with more participants.
Based on the image on the announcement page I'm guessing that a similar process will happen with an Ebonhawke contingent and an Awakened contingent. If so, the missions will evolve over the coming weeks to include new npcs. I would guess that there may be new missions as well, the graphic that showed outbreak locations had locations that weren't the current mission locations.
That's all my conjecture but it seems to fit with what we've seen and heard so far.