If 4-digit ratings are updated weekly and the 2-digit ratings updated quarterly, how will a tournament director know which rating to go by when setting up brackets?

The tournament registration software will use the 2-digit rating that was in place at the time the player registered. If a tournament director wants to accommodate player requests to use the rating on the days leading to the event, they are empowered to do so but are not required to adjust last minute as that can have a tremendous impact on draw sizes and partners.