You'll know everything completed when the syncing progress bars are gone from the app detail page. You can confirm this view by going to your Shopify store > Apps > ShopSync. If you see counts by the "Current Sync Status" area for products, customers and orders everything is done; you'll also see a total for promo codes.
If you're currently running Automations and pop-ups in Mailchimp, you'll want to migrate these after installing ShopSync. Mailchimp published a simple how-to article on the migration process in their Knowledge Base.
After your automations are migrated, disconnect the original Mailchimp for Shopify integration.
From your Shopify admin, go to Apps
Locate the 'Mailchimp for Shopify' app, and click the garbage can.
Go to the 'Connected Sites' area in Mailchimp.
Confirm that the store is removed.
If for any reason it is not removed, disconnect it.