After sharing a vault with others, I will continue adding to/editing the files in that vault. What does this mean for the people I’ve shared access with? Will they always see the updated version of my vault (including all edits and additions)?
It depends on the sync configuration.
Cryptomator does only the encryption, not the sync.
So if you are syncing your vault files constantly online, and the other people also, then the answer is yes.
A vault is nothing else than a bunch of files.