The reason for this is a missing registration inside your Azure portal that is underlying your o365 account.
In general your application requires this only for "One Drive For Business", therefore it works with 'Microsoft Account" One Drive.
It is mentioned in a side note on the One Drive SDK library Readme:
"For applications targeting OneDrive for Business call the class method [ODClient setActiveDirectoryAppId: redirectURL:] with specified and . Note: the redirect URL must match the redirect URL that you specified in the Azure Management Portal."
This is a multi-step procedure and is called "application registration" and you need to do the following steps:
1) Enter your o365 administration console and go to "Admin centers -> Azure AD". You basically enter Azure settings now.
2) Inside this special Azure view, go to "Azure Active Directory" -> "app registrations". Inside here create a new app by clicking on "new application registration".
From there you need to first create the app and most importantly insert the "sign-on URL" that was generated inside the "Application Registration Portal". After the app was created, you need to wait a bit (for me it was 10mins) until the app shows up in the list of "app registrations".
Once the app is registered you need to use another method to authenticate, see the text I copied from the SDK manual above: you need to use "setActiveDirectoryAppId" with a _new_ generated ID from the "app registrations" menu. This was the most confusing fact to learn for me! Instead of using the ID from the "Application registration portal", you need to provide this "application ID" from the Azure registration.
NOTE:
On top of that you can control the access rights for the application inside your Azure tenant. This is done by going to the "app registrations" list and click on the app and then on "settings". This overrules all other settings made anywhere else.
Good luck (I mean this in motivational way just as if talking to a soldier that was sent on a 'mission impossible' :-)).