How are No Man Sky Expedition initial appearance/equipment randomized?

The recent No Man’s Sky update introduced a new gameplay mode called Expedition.

Introducing a whole new game mode: Expeditions. Each of these events starts from a fixed point in the universe, bringing the whole community of travellers together to embark on a shared journey.
Each expedition is structured around a series of Milestones. Complete these unique exploration goals in any order as you earn rewards, meet up with fellow travellers, and experiment with new ways of playing No Man’s Sky.

Expeditions are assigned to separate game save slots. Apparently, Expeditions start from a fixed planet in the galaxy, and should follow a specific path, visiting specific "Rendezvous Planets"

Special Rendezvous Planets along the Expedition route create dynamic hubs of activity. Reunite with other travelers on the same journey, group up with the community to build a settlement, or simply wave hello as you pass through.

That said, the initial info I got mentioned that each Traveler would be assigned a random starting appearance, ship, multitool and so on. After the patch dropped I briefly tried the new mode on a separate user account on a Ps4 console and my initial appearance was an anomaly type.

A bugfix patch later I have started the Expedition. To my surprise, even after restarting the mode multiple time I always got the same initial configuration – a Vy’keen Traveler with red armor and red multitool… Must be an Atlas sponsorship.

Yet if you look at this Let’s play video

you can see that in this case the player seems to start on the same planet but with a different appearance from the one I got.

Since starting the expedition multiple times without saving always gave me the same character, I am wondering. How are expeditions seeded? It is the initial player appearance tied to the current console user playing the game? And in that case how are appearance randomized on the PC version – Windows user or something related to Steam maybe?