@fansy,
I hope someone else can help. What I think he is trying to say is that ". . . a sizable amount of buying" causes volume to increase. Here, he is simply repeating himself.
I can't imagine what he is means when he says that ". . . volume goes up and stocks react strongly one way or another." Not a gramatical issue, but he is saying that an increase in the number of shares bought and sold causes share prices to increase or decrease. It may be a true statement or not, but saying share prices will go up or down is not the least bit helpful.
I can't feel that I've been the least bit helpful, but I do share your confusion.