I will try to condense all the above issues and discussion.
The main question with this pool is what caused the two different types of discoloration.
1. One situation is a dark spot (that strongly suggests that acid or a Trichlor floater "etched" the surface in that location. The effect of acid dissolves and removes a top thin layer of plaster and expose the original plaster color (blue/grey) that hasn't been affected yet by anything else. Acid also causes a rough sandpaper like finish.
2. The other situation is that the blue color of the plaster appears to be changing or disappearing and turning to a predominent grey. It is very common to mix both a grey and blue color pigment for a special color appearance for pool plaster. Whenever the blue color disappears and leaves the grey unaffected, it is often because the blue pigment is not colorfast and therefore has been bleached out by either chlorine or sunlight. The grey color remains because it is has colorfast quality. And the plaster remains very smooth because no etching (from acid) has taken place.
3. A simple test can be done with acid to show what happens to the plaster and its' color. Just squirt some acid directly on the top step and watch the plaster fizz somewhat and the blue/grey color stays the same or becomes darker or more intense. A continual application of acid on the plaster will start to show the etching and sandpaper effect caused by too much acid being added.
4. Unfortunately, a similar test with liquid chlorine isn't likely going to show an immediately effect. That test requires some time. You could lower the water level of the pool to below the top step. Then sand a large portion of the step to expose unaffected plaster (and color), then pour some liquid chlorine on one half of the small area and not on to the other sanded area and wait a few days to see the results.
5. With regards to the suggested detrimental effects of using hard tap water to mix pool plaster, that is nonsense. Hard tap water generally only contains about 500 ppm to 1000 ppm of calcium. That isn't very much in reality. However, if the plaster company adds 2 percent or more of calcium chloride (as an hardening accelerator), that would be adding roughly 40,000 ppm of calcium to the mix water, and also a lot of chloride that can leach out of the plaster. Yes, that could cause a white efflorescence developing on the plaster surface.
6. While it may be interesting to know the current water test results, the reality in this case, is that much can be determined without knowing that as discussed above. I suggest looking closely and touching the plaster in the pool to determine if the entire plaster surface has been etched and is rough to the touch. Also note if there is any rough calcium scale on the surface. Also, ask the plasterer what was done to remedy the dark spot caused by the acid. That will help with this situation.
I hope this helps.