In SharePoint Online, when creating a root site collection with publishing site template the resulting outcome is an enterprise wiki site which obviously is not right. I should stress that this behaviour relates only to SharePoint Online part of Office365 offering.
Additionally, if the requirement is related to public facing website then this is not supported as described in the SharePoint Online Services Description document.

However, my requirement was relating to the private site collection (company intranet) which officially supports the publishing template. But as mentioned above I got the wiki site!
I got frustrated and raised a support ticket and question in the forum. To date this is still an issue.

So I had to resort to an alternative approach. I recreated the root site collection with team site template and activated publishing feature in site collection and subsites within them. That’s it. Why have the publishing site template as an option in the first place!?!
Needless to say that my requirement was met but frustrating with time consuming email exchanges and no sight of resolution. I shall update this post when Microsoft fixes the issue. Alternatively, if you know or hear then please add comments to this post or contact me. Thanks.

Curiously, when I asked Office365 support as to why I got wiki site instead of any other available sites. Their response was that in order to prevent the root site collection creation process in hanging state it was best to output the result as wiki site. Rest assured you did not select wiki site option by mistake!