See answer below re: OTP. Yes. We hoped the DNN would learn something close to an OTP. (The network we used for it is capable of learning an OTP, but the likelihood of doing so by gradient descent is vanishingly small.)
Nothing was shared between Alice & Bob except the secret key. The architecture of the three neural networks was the same (for Alice, Bob, and Eve), but they were all initialized independently and nothing was done to tie their weights together.
I wasn't clear from the article: Were Alice and Bob sharing any algorithm details, or was it just the secret key?