According to Consumer Reports they are the least expensive per load ($.22). I have very hard water as well and the tablets come with a built in water softener.
What do they use for the water softener?

I don't know...probably not phosphates.
We have a water softener for our house and it uses salt.
I went to the link you provided and at the bottom of the page there's another link for ingredients. Date at the bottom of that page is 2011-2013. Here's a list of ingredients.
Ingredients List
Ingredients Function
Sodium Bicarbonate Cleaning Agent- Builder
Sodium Carbonate Cleaning Agent - Alkalinity
Sodium Percarbonate Cleaning Agent - Bleaching Agent
Sodium Citrate (Dihydrate) Cleaning Agent- Builder
Polyethylene glycol Binding Agent
TAED Bleach Activator
Sodium Polyacrylate Antiredeposition Agent
Fatty Alcohol Polyglycolether Cleaning Agent
Microcrystalline Cellulose Filler
Protease Enzyme Cleaning Agent - Enzyme
Citric Acid (Anhydrous) Cleaning Agent - Organic Acid
Tetrasodium Etidronate Chelating Agent
Sodium Silicate Cleaning Agent - Alkalinity
Glycerin Solvent
Amylase Enzyme Cleaning Agent- Enzyme
Water Diluent
Fragrance Fragrance
D&C Red 7 Ca Lake Colorant
Magnesium Stearate Cosmetic Ingredient
Benzotriazol Preservative
Acid Blue 182 Colorant
Sodium Tripolyphosphate Cleaning Agent - Builder
Sodium Perborate Cleaning Agent - Bleach (Oxygen)
Sodium Silicates Cleaning Agent - Alkalinity
Zinc Sulfate Cleaning Agent
Product Page
No wonder the dishes are getting clean, they didn't take out the phosphates just reduced the amount in the product!
I pulled the ingredient info for the same product from July 2009. It's a pdf file so I can only link it. It lists sodium tripolyphosphate as the first ingredient while the new stuff (above) lists it closer to the bottom, meaning there is less of it in the product.
http://www.rb-msds.com.au/uploadedFiles/pdf/Finish Powerball Tablets-v9-31204.pdf
TSP, a little goes a long way baby!