You are correct -- they don't usually occur simultaneously. Usually, you would train and then test afterwards, but I've shown the test performance as a function of the number of training iterations, just so you can see what happens with generalization.

(Sometimes people do examine curves like this using validation data, so they can see when the best time to stop training is though)

The test loss goes back up because it classifies some of the test answers wrong. With more training iterations, it becomes more certain about it's answers (e.g., it pushes the likelihood of its chosen class from 0.9 to 0.99 to 0.999 etc.). For the training data, where the everything is classified correctly, that makes it more likely and decreases the loss. For the cases in the test data where its classified wrong, it makes it less likely, and so the loss starts to go back up.

Hope this helps. I will try to clarify in the book. It's always helpful to learn where people are getting confused.