The output of the neuron is computed as the activation function applied to the sum directly:
$$a_2 = h(w_{21}z_1 + w_{22}z_2 + \dots) $$$$z_3 = h(w_{21}z_1 + w_{22}z_2) $$
You can have a look at the perceptron wikipage, where there are explanations and ilustrations of this, like this one.