Segmentation of supporters and their synchronization
"We now want to email people who have take a specific action with an update on the campaign. I can see how to download that data from action on Campaignion, but is there a way to add or sync that data to Mailchimp supporter records about who has taken an action?"
This is done via tags. There are two ways of how your supporters get their tags:
If you edit or create an action, go to advanced settings at the bottom of your page and select "Auto segmentation", any tag you add here will be added to supporters who submit this action.
If you sort your supporters according to a certain activity (like taking part in an action) and then bulk tag them.
Integration with Mailchimp or Cleverreach
Tags should pop up in Mailchimp or Cleverreach without any further config necessary. However if you want to know which fields get synced, here is a list of them: What fields get syncronized in Mailchimp & Cleverreach?