I still hold to my original point: the registration and tracking, whether it's wizards or wands, only aplies to underage wizards.

Actually, though, it's not very accurate, is it? Because Dobby's magic got "assigned" to Harry in PoA. So it's not detecting wand use, because Dobby didn't use Harry's wand. Must be "magic in an area around a tracked wizardling". Which makes it rather unfair for Harry and Hermione and others summer-holidaying in Muggle environments: presumably juvenile Weasleys just claim it was their older brothers doing the magic.