I would add the queen when I made the split. If you wait to add her the split will start making queen cells and you would have to remove every one, or they will not accept the new queen. The split will know it is queenless in less than an hour after it is separated from the colony, but it will usually take 12 to 24 hours for the new queen to be accepted. Let the bees eat the candy and release the queen, if this takes 2 to 3 days, all the better as this gives the bees more time to get used to the new queen before they can get to her.
When requeening a full sized colony, I like to introduce the new queen to a 4 frame nuc and wait until she has been laying for 2 or 3 weeks, then I remove the old queen with 4 frames to a nuc box, and put the new queen's nuc in the brood nest area of the colony. I make sure the queen is on a frame in the center of the nuc. I keep the old queen as a backup until I am sure the new one is accepted.
When requeening a full sized colony, I like to introduce the new queen to a 4 frame nuc and wait until she has been laying for 2 or 3 weeks, then I remove the old queen with 4 frames to a nuc box, and put the new queen's nuc in the brood nest area of the colony. I make sure the queen is on a frame in the center of the nuc. I keep the old queen as a backup until I am sure the new one is accepted.