They use lateral ballast to tip the vessel before they release the logs. A good portion of the logs are already underwater before they are released, thus reducing the total weight change the vessel sees when the logs are released. Used to watch this from the air many years ago, what I remember is the rapid sideways movement. That is a lot of steel, in a high drag configuration, that gets moved laterally very quick.
I did see the aftermath of an unintentional side dump, ore of some sort off a barge tied alongside a freighter in Patricia Bay in about 1979. The barge rotated nearly 90 degrees, and shot straight up once the load can off. It came to rest partially on the deck of the freighter. Always wished I'd got a photo fof that.