Concrete – Can Half-Dried Concrete Be Refreshed by Mixing in Water?

You might want to contract a civil engineer to help keep the concrete people honest. If your engineer provides them with mix specification and makes test cylinders from each load, that should keep them on their toes (even if you don't follow though with testing the cylinders - they don't know if you will or you won't, so they have to assume you will - which they will be far more likely to assume if you have a site engineer and/or technician overseeing the pour and taking samples, rather than you trying to do that yourself.) If you have proper cylinders made by a certified technician and properly cured, you also have the option of hanging onto them and only paying for testing in the event that you have a failure of the pool and need to find out of the concrete was, in fact, up to snuff. Your engineer might also be able to offer you valuable advice that could either save you money or make your project more prone to succeed. They are not free, but they are often quite reasonably affordable, especially when considered as part of an expensive project.

The linked document also mentions measuring air content, which is generally how most "water reducers" work (adding additional air bubbles, which make the concrete flow better without as much water - and they have other, mostly beneficial effects.) So that's one way to verify that the water reducer has been used, rather than more water added. Again, this is probably best done by a technician with the proper tools, hired for the day via your engineer - and would be part of making test cylinders anyway.

Concrete obtains its strength due to the cement-water ratio. This means water is not a "relative" thing, but critical, in fact.

The fine and coarse aggregate (sand and stone) are basically just fillers. The space in between the aggregate needs to be filled with cement paste (cement and water). The more paste, the more cement you need.

A concrete mix design is based on the principles mentioned above. Depending on the source of your aggregate, your cement paste requirements may vary.

The "rule of thumb" ratios are based on experience, but don't guarantee a particular strength concrete.

A nice source of standard mixes for various requirements can be found at the South African Concrete Institute website