Yes, but in a different way than the other examples you cite. There is something called the sodium-potassium pump:
The other factor to bear in mind is that water tends to flow towards salts (sodium chloride and potassium chloride are both salts). This is why high-salt diets cause us to retain water.
Water flows (slowly) through cell membranes to whichever side has higher overall concentrations of sodium or potassium ions… so if the sodium/potassium balance changes, cellular pressure will change, until the body can compensate.
A sudden decrease in sodium can cause more fluid to move from the outside of the cell into the cell. (There’s more sodium outside the cell than inside, because of the sodium/potassium pump… and a decrease in sodium means the water will flow towards the potassium inside the cell.)
Alternately, a sudden increase in potassium will get into the cell, and once there, it will draw water to itself, inside the cell.
In both situations, the cell will tend to swell slightly. So if you rapidly go from a high-sodium, low-potassium diet (typical) to a low-sodium, high-potassium diet (like Soylent), you get a double-whammy. In sensitive tissues, it may be that this cellular swelling may result in a bit of pain similar to a dehydration headache. It just takes the body a little bit of time to adjust to the new (healthier) salt ratios, and for water pressures to rebalance.
Alternately, the problem may be more directly related to cellular signalling; cells have a resting “potential” or electrical gradient, and the sodium/potassium balance is important to the resting potential and therefore signalling. Again, the change in sodium/potassium balance may cause disturbances or pain sensations as the body adjusts.
Regardless the cause, it doesn’t last more than a few hours, and doesn’t seem to happen if you don’t have a very high ratio of sodium to potassium in you when you start on soylent. It’s possible that tapering into Soylent will avoid the problem entirely, even for those who are prone to it. By tapering, I don’t mean one meal per day of Soylent, which can still cause a headache after that meal. I mean having a bit of Soylent with one or two regular meals, as part of the meal - this will start getting your potassium up gradually before you start having meals consisting exclusively of Soylent.
After the first couple of meals, it doesn’t seem to happen any more (in my experience.)