If a player who earned a place in the Championship through Qualifying (i.e. non-exempt player) withdraws, the 1st Alternate from that same Qualifying Site will be contacted by the USGA to replace the withdrawn player. If the 1st Alternate declines, the 2nd Alternate from the same location will be contacted. If two players who earned their place in the Championship through Qualifying at the same location withdraw, both the 1st and 2nd Alternates will be contacted from that same site.
If an exempt player withdraws, the 1st Alternate from the next site listed on the reallotment list will be contacted by the USGA to replace the withdrawn player. If the 1st Alternate declines, the 2nd Alternate from the same location will be contacted. It is easiest to think of reallotment spots as allocated to a qualifying site, as opposed to by alternate.
Once an alternate accepts a place in the championship through the reallotment list, that site is moved to the bottom of the list.