I think for one CNN which they want to analyze, they train exactly one deconv net (in contrast to training one deconv net per layer). The featuers (inputs) of the deconv net are the activations of the layer they want to analyze. The output they train them on are the activations that actually was the input of the layer they want to analyze. So although they have one deconv-net in total, they train it layer-wise. So for each training run, the weights of only one deconv layer are adjusted.
However, I wonder why the images look that unrealistic:
Is it gray because MSE is the training objective? Why aren't the first layer filter outputs gray then, too?