One of the problems I see here is that 1st base was occupied by a baserunner with less than two outs and therefore this is no "dropped 3rd strike" situation, the batter would just be out. DTS is only in effect when 1st base is occupied with 2 outs. So not only did she not know the count (only 2 strikes), she also didn't know the situation that she shouldn't be running to 1st base because it was occupied.
I will agree that the plan to have them run to 1B on every strike 3 isn't perfect. In this case, some earlier intervention by the 1B coach might have been helpful.