You see, the moves have to be performed in the right order, and the Pokemon themselves, must be in the right formation. For it to work, you must meet the following:
(Opponent) <--> (Opponent) <--> (Opponent)
(Grass starter) <--> (Fire Starter) <--> (Water Starter)
(Must go first) (Must go second) (Must go third)
This is theoretical, of course, assuming that the order keeps going and going. In a realtime battle, if the Pokemon actually went in this order, then Grass + Fire oath would occur together, and then Water Oath would occur alone.