The minimized items area is not part of the RadTileView template - the positioning of the items is done in the ArrangeOverride method of the panel. You can pun an expander next to the RadTileView and in the handlers of the Collapsed and Expanded events you can set the MinimizedColumnWidth.
Could you please examine the attached project and if you have more questions please feel free to ask.
All the best,
the Telerik team
Register for the Q2 2011 What's New Webinar Week. Mark your calendar for the week starting July 18th and book your seat for a walk through of all the exciting stuff we will ship with the new release!