and has caused ALL the water woes you are having. He has in short errected a dam and also raised the level of the ground causing you to "pond".
You really have a all new problem that unless Jason can contridict, it will be your problem to re adjust since all the work has been on his property and sounds like nothing has damanged your land except for when it rains.
Cyprus mulch is what is always recommended for beds over all other because this type will NOT float. It sets down and stays there.
I am afraid that the problem caused by your neighbor is out of your control and you must re act to the situation and move the water out with his new additions.