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On raising a support ticket over this issue I learnt that Fastmail uses my work SMTP server to send these reminders (to my Fastmail email address!). I checked some recent reminders, and indeed, they have my work email address as the "From:" address, and they have been sent via my work SMTP server.
That is: Fastmail Calendar logs in to my work SMTP server as the "work me", whenever it wants to send me a reminder to my Fastmail email address.
If you have been---like me---working under the assumption that your personal Fastmail Calendar and your work email don't mix, it may be time to update that mental model. All your Calendar reminders may have been first sent to your workplace, before they come to you.