Your pool installer has done you no favors by recommending a tablet feeder. In it's natural state, chlorine is a gas. Many large commercial pools actually use gas injection systems to chlorinate their pools. Now, to change chlorine into something we can use at home it needs to be bound to something. The "somethings" that are commonly used are stabilizer (also known as CYA), calcium, lithium, or --- get this water. All of these add a little salt to your water, but they add something else. Cal-Hypo add calcium, Tri-Chlor and Di-Chlor (tabs and most granules) add stabilizer, Lithium hypochlorite adds lithium and liquid chlorine adds - water.
All of these things can be bad for your pool (except the water) in large quantities. The stabilizer helps shield the chlorine form UV degradation, but at higher levels it also impairs the ability of chlorine to do it's work. The higher the stabilizer level you have the higher the amount of chlorine you need. Too much calcium and you start to get scaling on the walls and floors of your pool.
Calcium, this leads to a second comment to you. You live in a high calcium area. Meaning the water that comes out of your hose is high in calcium naturally. Most pools in the southwest US have slowly rising levels of calcium (CH is how we refer to it) which needs to be watched also.
For a new pool I would be eliminating the tab feeder and going with a salt water chlorine generator. Please do not be confused as many are that "salt" is a sanitation method. Salt is placed in a salt water pool to create chlorine. The same chlorine I was talking about above. In a salt pool there is a device, called a salt water chlorine generator (SWG or SWCG). Through a chemical reaction in the devise chlorine gas is produced in the water flowing through it. This constantly adds chlorine to the water. Then, through he process of sanitizing your pool the chlorine breaks back down into salt and the cycle continues.
All of this leads to testing. Order a
TF100 test kit. That probably will give you enough reagents for a couple of years normal use.