I ended up at https://$mydomain.1password.com/integrations/directory and I can only see Fastmail as an option. Clicking there it asks me to Connect with Fastmail rather than that I can provide my own domain. I already have a wildcard domain setup so I'd like to use it as @davzie mentioned.
You need to OAuth to Fastmail (the service) to hook it up, then as was mentioned above, you can go into the settings in your Fastmail account to choose which domain your Masked Email addresses are created in:
Settings -> Domains -> Team Settings -> Masked email domain
It will default to fastmail.com, but easy to change it.
Oh, I completely misunderstood then, I thought I could do this with just 1Password. I already have email setup myself and don't need Fastmail, so then it seems I cannot use this feature. I'll just continue myself to randomly generate my addresses then...
Well, as I understand it you'd have to do this manually. As in, pick a random alias for the site, use that as you email address there and enter the same one in 1password (or any other credential store).
The full "it just works" integration seems to only work between 1password and fastmail directly.