Oh, when using pool water as a starting point, you will get CYA initially so that's good. The TA is probably higher than you'd want for a spa because as you've noticed between the hotter water temperature and the greater aeration, there is more carbon dioxide outgassing so the pH rises faster. If your spa as its own separate circulation isolated from the pool, then you should be able to manage it just as you would a separate spa.
Note that unlike your pool, with a spa you have to dose with a good deal of chlorine after each soak. The bather load is far higher in a spa because of the smaller water volume. Without an ozonator, each person-hour in a hot (104ºF) spa requires around 5 fluid ounces of 6% bleach (3.6 fluid ounces of 8.25% bleach) to oxidize the bather waste, though you should just use whatever amount gets you to around 1-2 ppm FC for the start of your next soak. You usually target a lower starting FC to reduce chlorine/chloramine smell during your soak. You can go higher if you want to, but no lower, and you must dose right after your soak.