how is correct usage of the validation split in neural networks?

I really like this post with the answer on your question.

Once we have the estimated skill, we are finished with the resampling method.

You finalize a model by applying the chosen machine learning procedure on all of your data.

It means that after achieving enough performance of the model, we don't need anymore splitting ("resampling methods"). Then we can merge all available data and repeat learning procedure. We can rely on the final performance (have no qualms about, who model will behave using new data during training), because it has already learned how to generalized input for the particular task (differ cats from dogs for example).

The careful design of your test harness is so absolutely critical in applied machine learning. A more robust test harness will allow you to lean on the estimated performance all the more.