Make sure to add the necessary domain names to your Intranet zone in Internet Explorer. The default settings in the intranet zone ensure that all cloud-based applications run with the same permissions and configurations as your internal, on-prem, applications.
In case you want to enable single sign-on to Office 365, please make sure that the Internet Explorer setting User Authentication \ Logon is set to Automatic logon only in Intranet zone or Automatic logon with current user name and password.