It looks similar to the description of the bridge being built in "World without End" by Ken Follett. One bit that is missing from this animation is that there is no rubble placed in the water around the piers. In the book this had the all important function of preventing the foundations from being washed out by the river. Maybe that was fiction or it was too much detail for the animators since the water is not transp…
i.e. once the water is out of the enclosure, you have a surface that is likely to be soft wet mud or sand. Surely you want to scoop some out, dig down and lay some big blocks of stone under the river bed level?
Or maybe that happens, but was just not shown. Or maybe, once you start building up, the sheer weight pushes the whole column down until it settles.