Which integration are you using? If it’s the one that runs on Zapier then I don’t think it syncs data from AT > MC (but only the other way around).
And a brazen plug: we’re just adding final touches to our Airtable - MailChimp integration. This would let you sync contacts from AT to MC with custom field mapping, and mapping to a MC tag would also be possible. If this sounds interesting sign up for early access here