For Wartime Economy, the v3 rules specify that « Each turn during its Place Units and Collect Income Phase, the nation rolls 2D6… » and « British Commonwealth may divide the money each turn… » (rule 7.8 & Global War Tech Sheet v3.0).
« Each turn » must mean the same in both sentences, so if you do it by the book, you would divide it between Commonwealth members during that same phase, not set it aside as a pool for the next purchasing phase.
However, in a friendly game, I would probably let the Commonwealth player redistribute the Wartime Economy as needed for purchases to speed things along.