Thanks for the drawing!
It looks as though this tool (expertly illustrated) is a puller tool rather than a pusher. I'm guessing it would be used like this one - http://www.ebay.co.uk/itm/Sealey-VS801- ... 5d4f768ae9
If you scroll down through the advert there's a small illustration showing it in use at the bottom (this tool is for hollow pins. Viva HB hinge pins are solid with a pin head that the 'U' end of the tool would fit under).