That is an incorrect assumption because, separate from moving the messages to the Spam mailbox, FastMail can mark in the message’s headers that it thinks it’s spam (but not spammy enough to move it). It’s also possible that it’s setting the IMAP junk flag.
By the way, could you clarify what you mean when you say that the message is flagged as spam in MailMate? Is there a number for the Spam Score?