It's always the player's right to take half, but in all the calcuttas I've been to, and that is a whole bunch of them in many cities and states, I can't recall the auctioneer immediately asking the player if they want their half each time each and every time they get sold during the auction.
It makes me wonder if they are doing it in that area because they have had a problem with one or more bidders trying to pull some moves, like ducking out and trying to avoid the player they bought until after the tournament starts so they don't have to give up half to them, and then trying to say "well the player never came to me and asked" or some other similar type situation, and so the auctioneer now does this to prevent that bidder/s from being able to try to pull their move. And maybe it is a high action bidder/s that bids big and they don't want to just ban him/them, or they are scared of them, etc.
Whatever that calcutta auctioneer's reason for asking each and every player if he wants his half immediately after he is sold, it is not what is typically done most places.