They are both wrong. The proper way to lower the TA is through a combination of lowering the pool's overall pH combined with aeration of the water and further addition of acid to keep the pH low. The procedure is described in this post
. The pool stores and many pool service and installation professionals mistakenly think that the "slug" or "acid column" method is the way to lower the TA. This is debunked technically and with field data in this document
You should always add acid VERY slowly over a return flow at the deep end with the pump running and then lightly brush the side and bottom of the pool in the area where you have added the acid. That way, you thoroughly mix the acid -- it's VERY strong and concentrated and you don't want it to settle (it's denser than water unless mixed). The same approach should be used for adding other chemicals such as chlorinating liquid or bleach to the pool (or Dichlor, for that matter -- Cal-Hypo is best mixed in a bucket beforehand and then poured as with other chemicals over a return flow). The only exceptions are with PolyQuat algaecide (and concentrated clarifiers) which is thick so needs to be dispersed around the pool and with Cyanuric Acid (CYA) which is slow to dissolve and can be added either slowly in the skimmer to get caught in the filter (and take up to a week to fully dissolve) or be put in a sock or panty hose and hung over a return flow (takes a couple of days to dissolve). Obviously, slow-dissolving products like Trichlor are used in floating feeders or inline chlorinators or sometimes with special versions (BioGuard Smart Stick) in the skimmer.
To aerate the water, turn on any water features you may have such as waterfalls, fountains, aerating jets, spillovers, etc. You can turn up your return "eyeballs" to point upward so water agitates the surface. You can also use this fountain device
or this air injector device
. If you have an air compressor and have a nozzle with many small holes, then putting that hose end into the deep end and running the compressor will aerate the water a lot and make the process go much faster.
Pools are intentionally over-carbonated (like a carbonated tasty beverage! though obviously not that carbonated) in order to provide a pH buffer and to protect pool plaster by saturating the water with calcium carbonate. The carbonates in the water are just that -- carbonation -- the result of dissolving carbon dioxide in the water. Adding baking soda (sodium bicarbonate; sold as Alkalinity Up in pool stores) adds bicarbonate to the pool which is in essence a form of dissolved carbon dioxide. The ONLY way for TA to get lowered permanently (rather than via the see-saw with pH) is to remove some of the carbonates from the water and that is done by aerating the water to drive out some of the carbon dioxide since it's at a much higher concentration in pool water than in the air. This process of carbon dioxide outgassing goes much faster at lower pH with relative rates as shown in this chart
The slug or acid column method only partially works by lowering the overall pH, but if you don't keep the pH low and add more aeration, the process takes much longer. Technically, you could just not do anything but add acid to keep your pH in the normal range and very slowly over time your TA will get lower. It takes the same total amount of acid to lower the TA regardless of method -- the only difference is in the speed of TA drop. Of course, once the TA is lower, the rate of pH rise is also lower which is one reason to have a lower TA so that you don't have to add acid as frequently to maintain a proper pH.
It takes a LOT of acid to lower the TA -- much more than the initial amount that is added to lower the pH to 7.0 or 7.2 when you being your aeration. I can tell you how much acid you will need if you give me more info such as pool size in gallons, current pH and TA levels. Also tell me if the lowest reading on your accurate pH test (using phenol red indicator) is 6.8 or 7.0.