The rubber seat insert and the all metal needle does go in some these carburetors.
Please review the images in the following link for more info, Items 15 thru 18 show the use of this system.>
http://outdoorpowerinfo.com/repairs/briggs_medium_two_piece.asp
Also note that the rubber seat usually have a groove in it which goes toward the bottom of brass seat; away from the needle itself.