On-premises users in an Exchange hybrid deployment are unable to see MailTips of Exchange Online users by using Microsoft Outlook 2010. However, they can view the free/busy information of Exchange Online users.
This problem occurs if the user configured their mailbox to deliver messages directly to a .pst file. MailTips aren't displayed in Outlook 2010 if a .pst file is set as the default delivery location.
Configure Outlook 2010 to deliver messages directly to the user's mailbox instead of to a .pst file.