Is it a condition for water to reach the area of impurity that has extended beyond its usual place for the bidet water to reach it directly, or is it sufficient to move the hand to deliver the water to it?

If you wash the impurity with a bidet sprayer and rub it with your hand, the impure area becomes pure when water reaches it and the impurity is removed, even if the water does not reach your entire hand. For istinja' (cleaning oneself after relieving oneself), it is sufficient to be reasonably certain that the impurity has been removed and the area is clean. Certainty is not required, as requiring it would be a hardship. One must be wary of obsessive thoughts (waswas).