Maybe the language here is causing confusion.
Imagine a skeleton (as in an undead monster) that is lying on the floor. In this state the skeleton is (mostly) indistinguishable from just a regular, non-undead skeleton. Just a bunch of bones.
Then, when something provides a stimulus for the undead skeleton (e.g. when someone approaches; this stimulus can vary), it rises, it stands up. That's when the everyday adventurer notices that it's an undead monster that should be destroyed.
So when the adventure says, "are animated", it could be just a descriptive way of saying, "stand up to act". It may not have anything to do with the concepts of reanimation.
If a Paladin uses Divine Sense near the skeletons, are they considered undead? Or are they regular skeletons before the "reanimation"?
A normal, non-undead skeletal remains isn't undead, but an undead monster called a skeleton is.
As far as I understand it, reanimation is what turns a corpse into an undead creature. Before reanimation, it's a corpse; afterwards it's an undead.
So the key to this question is, what does "are animated" mean?
If it's just a descriptive way of saying that the undead skeletons become livelier than usual and start acting, then they've been undead all along. (And they ping in Divine Sense, and so forth.)
If it means that there's some necromantic magic around that animates skeletal remains into undead skeletons, then they become undead the moment that magic is finished turning them into skeletons.
I'm sure you'll agree that the first option makes more sense, at least in this context. After all, it's easier to explain that three skeletons have been made selective in when they rise and act, than it is to explain how some necromantic magic can selectively reanimate a bunch of corpses at once.