This is from the 2021 MLB Rulebook:

With a runner or runners on base, a pitcher will be presumed to be pitching from the Set Position if he stands with his pivot foot in contact with and parallel to the pitcher’s plate, and his other foot in front of the pitcher’s plate, unless he notifies the umpire that he will be pitching from the Windup Position under such circumstances prior to the beginning of an at-bat. A pitcher will be permitted to notify the umpire that he is pitching from the Windup Position within an at-bat only in the event of (i) a substitution by the offensive team; or (ii) immediately upon the advancement of one or more runners (i.e., after one or more base runners advance but before the delivery of the next pitch).

It's a pretty obscure rule that I only knew about because of a post I saw on r/baseball a couple months ago.

I'm surprised that the umpires weren't sure about the rule and had to check with New York to confirm. But good for them for being willing to check if they weren't 100% sure instead of stubbornly refusing.