The payout schedule for the Vault Tour is found at https://www.fantasyflightgames.com/en/news/2019/3/6/the-hunt-for-aember/

I can't figure out what counts towards earning Aembershards.

It says 30 shards for participation. Participating in what? Each individual tournament? Just the "main event"? Just the first tournament you're in?

Same thing for wins, and placing-- per tournament, just the main event, or what?

If it's just the main event, they really should say so on the page. And if the printed figures are only for the main event on Saturday, does that mean you get literally *nothing* for participating in the many other tournaments that they're hosting at the Vault Tour-- like, showing up to a 4 person event at the local gaming store awards shards, but going to a different state to attend the vault tour and playing in a 16 person tournament doesn't?

Here is info from Cascade Games running the Vault Tour events from their FB Event post for Seattle Vault Tour:

Prizes for the main event will be given in Aembershards. The winner of the event will receive free travel and accommodation to another US Vault Tour of their choice. Aembershards are given out as follows…
- 30 for participation
- 15 per win
- 500 for the overall winner
- There are also additional shards to be given if you make the cut depending on which round you are eliminated
For the main event Aember is added to your account at the end of each tournament day (approximately 30 minutes after the last round concludes as we'll need to wait for the last games to finish, enter results and upload etc...).
Players must have access to their Mastervault App for their Player Profile QR Code. We strongly recommend taking a screenshot of your player QR code in the case that you do not have mobile internet at the convention hall. Sealed Decks will be handed out at the start of the event and registered after the player has chosen 1 of their 3 decks to play in the Main Event.

Side Events:
Side events will run each day. The first side events will begin at 10:00am. Players will need to come to the Registration and Prize Wall area in order to register. Each side event awards Aembershards as prizing as follows and Aember is added to your account after the conclusion of the side event...
Archon/Sealed Pod Events get you...
- 2 for participating
- 5 Aember per win
(This will give you a maximum Aember per pod of 17!)
Scheduled side events are 4 rounds each and get you...
- 3 for participating
- 0 additional shards if you end up 0-4
- 5 additional shards if you end up 1-3
- 10 additional shards if you end up 2-2
- 20 additional shards if you end up 3-1
- 40 additional shards if you end up 4-0
(This will give you a maximum Aember of 43!)
Aember is added to your account after the conclusion of the event

Didn’t know about this cool!