Alkalinity up is baking soda with some extra fillers. The only thing that one would "need" from alk up is the sodium bicarbonate. The rest of the formulation is irrelevant.
Soda ash (washing soda) will raise pH and TA. Borax will raise pH with a minimal effect on TA.
When your TA is is good, the pH rise tends to be much slower than it would if the TA is high. My pool likes the TA right around 70 and when it is there, I only need to add a little acid once a week. Generally, the TA will fall over time from acid additions to lower pH and it will come to rest at a spot that it likes. Of course, if your fill water has a high TA, then this can hamper that process. I just know that I never have to adjust the TA in my pool. It stays at 70 as long as I keep my pH under control.