Beginning with Office 2016 Outlook auto-connects to 365 upon opening. This causes users to be prompted for credentials if their account is on-premise. To disable this, run this in PowerShell as the user:
Set-ItemProperty -Path HKCU:\software\Microsoft\Office\16.0\Outlook\AutoDiscover -Name ‘ExcludeExplicitO365Endpoint’ -Value 1 -Type DWord -Force