There are many reasons why your emails may not be syncing into Mailchimp directly.
1) Emails you receive only sync to your list if they signed up AFTER the integration was done.
So if you got a bunch of signups on your contest, then you went to integrate with Mailchimp, the emails that have already signed up won't get automatically pushed. You'll need to use the export CSV function to manually add the emails into Mailchimp. That's why we recommend you adding the integration FIRST before you set your contest live.
2) Emails may have already been on your list, or they may have previously unsubscribed.
If anyone is already on your list, they won't get added again. This also applies to emails who have added themselves and unsubscribed. They can't be re-added to your list.
3) Mailchimp takes a while to get their numbers correct.
If you're only looking at the numbers, they may not be accurate. Instead take a look at the recent subscribers of that list. Step by step instructions below.