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A normal sprinkler works by a pump pushing water out the nozzle. Wouldn't a time reversed sprinkler be a situation where water is flying into the sprinkler and depressing the pump? in that case I would expect the rotation to be reversed.

Well, yes. Isn’t that the situation the article is describing? Suction isn’t a real thing, so-

Wait. Is this meant to imply it’s running underwater?

Yes, in the thought experiment it runs underwater. It's fine though because it can run underwater in both cases, so that doesn't ruin the symmetry.

The article implies a situation where the pump is running in the opposite direction as normal, sucking the water in. That's not time-reversed though (eg in the time reversed version, the pump generates electricity instead of consuming it, because the water is pushing it instead of it pushing the water)

No. A nozzle behaves differently if you plug it the other way around, and that does not break CPT symmetry.

The rotation is not reversed though (at least not with the same speed), that's why it's always been interesting.