How high was the pH before you added acid? It sounds like it was only like 7.4 and you added enough acid to get it down to 7.2. In this case, the effect on TA would be quite small. You want the pH somewhere above 7.6 and add enough acid to get pH down to 7.0-7.2 to have a significant effect on TA. And then repeat this a few times.
Could it be that you didn't run the pump long enough before testing pH and TA? You might have tested in an area with a higher acid concentration, where the local TA was lower. Once the acid was properly mixed in, you saw the real TA. That's the only way how TA might appear (!!!) to rise back up again. TA can only rise by adding fill water with a TA higher than the pool water, or by adding a chemical like baking soda that increases TA.
If you are having problems to get pH above 7.6, then there is actually no urgency to lower TA, unless you have really high CH and you need low TA to get CSI under control. Otherwise, lowering TA is only required if pH keeps drifting up too quickly. There is no need to force TA down unless you have one of those two problems.
Are you adding any form of chlorine at the moment? Having enough FC in the water is your number one priority. Before worrying about TA, make sure that you have enough chlorine according to the FC/CYA chart:
Managing your cyanuric acid and Free Chlorine levels is key to stabilizing your pool. Learn how these two items affect each other.
www.troublefreepool.com
Use liquid chlorine until you can run the SWG.
Just to confirm the kit you are using: Do you have the Taylor K-2006 or the K-2000? The K-2000 is only a very basic FC/pH kit - that doesn't really make sense as it doesn't have a TA test. You need the K-2006. If you have the K-2005, then you'd still need an add-on FAS/DPD test for the TFP method. Only FAS/DPD has the required precision and allows to measure SLAM-levels - DPD alone is not sufficient.