Syncing SharePoint folders

I've not seen nor discovered a means of syncing sub-folders in SharePoint Online. What you're experiencing is normal behavior for SharePoint Online, and I don't believe there to be a configuration item to make that functionality different (yet, anyway, who knows what could happen later on).

As an alternative/coping mechanism, I would suggest taking a look at how your organization will plan to use Document Libraries; namely, how many document libraries within a site you'll plan on using. We've had departments at my organization separate their documents by certain criteria (like security or purpose of those documents) to make syncing a bit more palatable.

Best of luck in your transition!