Couple things here. Your pH is rising because of the TA in the water. The carbonic hardness (TA) of the fill water wants to turn into carbon dioxide which then offgasses. This offgasses, and therefore the entire process, happens much faster with aeration. As the carbonics turn into CO2, they raise the pH of the water. I don't have the chemical equation handy to show how, but that's how adding low pH water can raise the pH of your spa.
Secondly, you by no means have to lower the pH to 7.0-7.2 to lower your TA! Any acid addition at any pH will lower your TA. If you want to lower your TA from 80 to 50, use poolmath to calculate the amount of acid you need to add, then add the acid. I think you have the pH of 7 stuck in your head because when doing a major TA reduction (like from 250 to 50), adding enough acid to lower the TA that much would drop the pH very, very low until aeration could raise it back up. This low pH, perhaps less than 6, can damage pool equipment. Hence why the instructions say to add acid to lower the pH to 7, then aerate and repeat. And by no means do you have to lower it to 7 when doing a major TA reduction either, you could lower to 7.5 each time, it just means it'll take longer to do the TA reduction.
So in short, going to 7 is for major TA reductions and is just to avoid equipment damage from huge acid additions. Going from 80 to 50 this won't be a concern though.
Add the acid poolmath says to drop your TA from 80 to 50. Then aerate for 30 minutes and retest your pH and TA.
EDIT: Actually it would be good to add about 3/4 the amount of acid poolmath says, aerate and check. Then if you're on track you can add the other 1/4 or adjust if needed. This way you don't overshoot the 50 TA mark and have to add baking soda to bring it back up because your pH is sitting at 7. Ask me how I know!
