Hi Brice,
At present, the OneDrive for Business sync client is only available for the PC. And in the near future, the OneDrive for Business sync app will be released for Mac OS. And you may bookmark the following website, because most of the updates for Office 365 for business are listed inside:
http://office.microsoft.com/en-us/products/office-365-roadmap-FX104343353.aspx
Meanwhile, on Mac, we may also use the SharePoint Workspace application to sync contents temporarily.
In your situation, regarding “We have OneDrive downloaded on the Mac”, it seems it is the OneDrive sync client instead of the OneDrive for Business.
Actually, the OneDrive for Business storage service is different from OneDrive storage service.
For more information, please see: How is OneDrive for Business different from OneDrive?.
Regards,
Charles