"Creature does not untap" on Mutavault
No, it won't untap. &quot;Those creatures&quot; is not a check. It's just a nice way of saying &quot;those objects that were targeted&quot;. Any later changes to the object's characteristics are irrelevant.

608.2i If an ability’s effect refers to a specific untargeted object that has been previously referred to by that ability’s cost or trigger condition, it still affects that object even if the object has changed characteristics.
Example: Wall of Tears says “Whenever Wall of Tears blocks a creature, return that creature to its owner’s hand at end of combat.” If Wall of Tears blocks a creature, then that creature ceases to be a creature before the triggered ability resolves, the permanent will still be returned to its owner’s hand.


A note on &quot;untargeted&quot;
It seems to me that &quot;specific untargeted object&quot; refers to phrases like &quot;that something&quot; or &quot;those somethings&quot;, even if they are short for &quot;that targeted something&quot; or &quot;those targeted somethings&quot;. The word &quot;untargeted&quot; is there to exclude &quot;target something&quot; and &quot;target somethings&quot; from being covered by 608.2i since targets are rechecked on resolution.
There are two cards that cannot shorten &quot;that targeted creature&quot; to &quot;that creature&quot; without becoming ambiguous. &quot;That targeted creature&quot; does not target, so 608.2i does apply.