Yes - only one domain is the primary/default, you go into their Aliases section and have to set up a foo@domain1.com to foo@domain2.com mapping (if you use the add domain wizard it makes it for you). You still need to set up your DNS records for the second domain like the first.
(I bought two domains and did exactly what you're asking - after using the first for a day or so, having decided I liked the other one better I reached in and simply flipped the dropdown and chose the second one to by the default, clicked OK and it all just worked nicely)
When I look at my set message headers, it would appear that your primary @fastmail.com (or whichever of their domains you choose) is your actual primary, and that even your first domain is just an alias to the actual user account domain.
For what it's worth I have found Fastmail's documentation to be really good. Whenever I had to look up things like configuring email clients or their spam rules I have been pleasantly surprised.
Not sure if this answers your question specifically. But yes, they do allow for domain aliases. I specifically use their wild card alias. For example, let's say I own the domain `mydomain.com`. Fastmail allows me to have `contact@mydomain.com`, `apple@mydomain.com`, `linkedin@mydomain.com`, etc. on the fly.
Nice. Thinking about it more, I think I could live without it but I have it with Gmail at the moment. I like the per-address basis though, in Gmail I add the domain alias then when I add an email alias that alias applies to all the domains.
EDIT: They do. https://www.fastmail.com/help/receive/domains.html#mirrored