You need to get your $:/yourname/TiddlerTypeTemplates/Contact tiddler before $:/core/ui/ViewTemplate/body in the list field of $:/tags/ViewTemplate. The easiest way to do this is to click the tag pill for $:/tags/ViewTemplate where it appears on your $:/yourname/TiddlerTypeTemplates/Contact tiddler and drag and drop the entries into the proper position.

You could also manually edit the list field, or even create a <<list-links-draggable>> or <<list-tagged-draggable>> macro to reorder the members of the tag.