Yes, they can do an acid wash even with water in the pool. I've seen some good results.

"however he did state that when you mix cement and colors you can get areas like this. He think's it normal."

No, that's not true. Can you post a pic so we can see how big and how white are the spots you're talking about?

Here is a photo, if you look at the wall you will see.

Here is one more photo of the steps, you can see some sports there also. I believe the darker area is what it should look like, it seems like you can see the pebble better in the darker areas. Like they didn't use enough acid to expose the pebbles when they resurfaced the pool.

This is totally normal. This is actually the hardest part of selling a colored interior surface - convincing the pool owner that it will look great in 2-3 years. What you are looking at is the portland cement, and you are correct that more acid will remove it, and there is the problem. You are not supposed to acid wash a pool right after you plaster it. This strips all that silky portland cement away and leaves only the aggregate. The aggregate is colored, and that is what you want to see, but forcing this to appear early with acid is actually bad for the plaster. As a pool company you only acid wash to appease the customer. It makes the pool feel MUCH rougher. Further to this, most pool guys use way too much acid. An acid wash of a colored surface should be around 7-10 to 1 so that the acid barely even foams when you put it on. Most of the cleaning should actually be done with acid brooms, not acid strength. Unfortunately pool owners want that fantastic color that they paid a lot of money for so the pool guys end up acid washing much stronger than they should. If you choose color in your plaster then it will look like this for 1-3 years. If you want it to look better, faster, then you can acid wash the heck out of it...the only problem is that your brand new plaster will now look and feel like 5 year old plaster. The real problem here is that your pool contractor did not take the time to explain all of this to you so you were surprised by the results.