Is it the salivary glands going into overdrive?
This makes sense. The major salivary glands are under the tongue and in the cheek area, but there are small salivary or mucous glands in the hard and soft palate, buried within the muscle tissue. If these glands fill with newly-made secretions faster than they can release secretions into the mouth, then the glands will swell up. They don't have a lot of room to expand, so that may be causing the pressure and pain, which is relieved relatively quickly (10 minutes?) as the secretions move out.
Maybe plain water is a weaker stimulus for these secretions than the acid/salt/sugar/fat chemicals in our food, and this could explain why drinking water first after the fast prevents the development of pain that occurs when we eat other foods first.
We are dehydrated after a fast, and it's good to rehydrate right away, but I don't see how the pain in the palate would be related to overall dehydration/rehydration.