It means literally that but it means to settle in and prepare for something bad stressful to happen, which you are going to weather (e.g. a storm), or to close in around something and get close to it or other people around you (e.g. around a fire), especially if it evokes a feeling of solidarity or safety. E.g. the kids hunkered down around the campfire and told stories to each other or, they hunkered down in their bunker, watching the news. So the first one works if he's really intensely washing his hair, but the second one doesn't work because it's really not (usually) a stressful situation. If, unusually, it is going to be, then you can use hunker down there too.