Outlook.com accounts that are not migrated to the Office 365 infrastructure will not be able to sync with FullContact. In essence, eventually all Outlook.com accounts will be migrated to the Office 365 infrastructure, but not all have been migrated yet.
One indicator of whether your Outlook.com account has been migrated is what shows up in the top left in your Outlook Web App (OWA). Migrated accounts will show “Outlook People.” Unmigrated will show just “People.”
Another indicator is the URL of your Outlook Web App (OWA). Unmigrated accounts use URLs similar to something.mail.live.com and people.live.com. Migrated Outlook.com accounts use outlook.live.com.
If your account is not yet migrated to the Office 365 infrastructure, you will need to wait until your account is migrated by Microsoft in order to sync with FullContact. Unfortunately, we are not aware of any public timeline for when all Outlook.com accounts will be migrated.
Note that newly-created @outlook.com accounts are migrated automatically. However, newly-created accounts in other Microsoft domains, such as outlook.___ (Outlook accounts with other TLDs), are still unmigrated.