It is a one year shore-tour post Department-Head.
War college doesn't actually have to be post DH. It just usually falls there because you don't have time in your career before then for most aviation warfares. SWOs (from my understanding) have so much extra time in their career that they can do lots of things like this that aviators cannot. As a carrier pilot, you have no chance at being an ROTC instructor, so if you want a masters, it's going to be on your own time. If you took a long time to get through flight school, you won't have time pre-DH to get War College (and they probably won't send you unless you got #1 out of a big place like a RAG). Post DH, you have to be able to do a joint tour, and with year groups in the F/A community dragging people up by the fistfuls, you are losing 1-2 years off of your career path before you are up for command, so you have even less time to squeeze anything in. Throw an IA in there to use up another year of your career while not buying you any checks in the box (maybe some joint credit if you're lucky), and you are basically working your ass off as a DH while doing your distance JPME and trying to get a masters on top.
I'm all about being competitive, but I believe that if the Navy wants you to have JPME, they should build it into your career path. I think that if they want you to have a Masters, they should build it into your career path. I nearly have a Masters on my own because I just am a nerd and like to abuse myself in my off time, but I don't think that should be the way people do it. Some people actually have a life away from work, and they shouldn't be penalized if they are a good pilot/officer. We have way too many douches that suck in the jet, suck at leading, but are really good at putting their efforts into JPME and their Masters while everybody else picks up their slack. They get the checks in the box, and the guys that fight wars have to get out.
I do know that there is a good reason for JPME, and i do believe leaders need to be well-rounded (especially above the O-5 level). BUT, there are ways to train your people without making them do it on their own or flail.