[Moonman62]

Do they operate cranes in the middle of the night? How about when there’s severe storms in the area or a during a tornado warning?

[Hot Tabasco]

Do they operate cranes in the middle of the night?

In big cities, yes they do so as to minimize their impact on daytime traffic........

[Svartalfiar]

Do they operate cranes in the middle of the night? How about when there’s severe storms in the area or a during a tornado warning?

Nighttime, sure. After midnight? (Per article, it was two tornadoes "after midnight".) I don't think that late unless there's a major incentive of some sort for early project completion.

But yea, they shouldn't be doing much of anything in any storms. Tornadoes don't usually just appear on their own, there's a bunch of thunder and lightning and wind and rain that comes out before and around them!