UPDATED 11/02/2015

It has been a long wait and lot of pain, but finally we got it!!! The NEW button on a document library now shows the custom content type you may have defined for this document library.

UPDATE if you have enabled custom type (and so display these content type in lieu of the defaults one), the New Folder option which is available with defaut content type disappear. The SPO support engineeer explained to me that the custom content type replace what is displayed; so if you want to have a New Folder option available when you are using custom content type, you need to create a new site content type for the folder too

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Until then, the only way to get the custom content type was to use the NEW button from the Ribbon.

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BUT, wait, there is still an issue Sad smile; if you display the content of the document library using a webpart on a web page (let say the home page), the NEW button does not show (yet?) the custom content type – I have raised a ticket for this (as I did for getting the content type using the NEW button)