Well we can think in this direction:
for the precipitate formation we have to have a precipitate nuclei (nucleization process), for this we need to have at least several ions (according to someone more than 2000 but this is not so important here) and the chances for this "meeting" are greater on the walls of the tube.
When we have huge volume in one tube the interaction within the solution and the wall is smaller compared with the situation when we have several smaller tubes with smaller volume inside.
That so the precipitation is faster.