American Standard made several different versions of the tilting flush mechanism. You have the wrong one for that toilet. The proper one has a hollow on one side of the "float" and the other side is closed. By having only half of the floatation, it stays shut when the water is filling. What you describe will also happen if the toilet is plugged and fills with water. Lift the seat when you flush the toilet to see if it is actually flushing properly.