The Cheshire does not lie. Your collimation is off (if I read what you're saying and your diagram correctly). Just adjust the primary till the cross hairs line up. If that doesn't do it, your secondary is too far off.
Note that there should be some overall offset because of the way a Newtonian works (I assume you're talking about a Newt). But the x-hairs, its reflection and centre spot should all be aligned. I'll try and find a link to a good article for you that explains this and will edit my post when I do...
This article explains well how to do the collimation:
http://www.skyandtelescope.com/astro...tor-telescope/
... but it does not show the final secondary offset inherent in Newtonian geometry. But if you follow the instructions you'll have a well collimated scope (the star test at the end is not normally necessary, but if you have enough seeing, it's a good way to check things).
This article explains secondary offset (which will pretty much take care of itself automatically if you follow the collimation procedure correctly):
http://www.skyandtelescope.com/astro...ondary-mirror/
... but it does not show how things should look through the Cheshire when you're done.
Maybe someone else has a better link.