Ideally, the CH should not rise at all because you will have created a water-tight calcium carbonate seal in the plaster surface. Again, the purpose of the bicarbonate startup is to convert the calcium hydroxide produced during curing into calcium carbonate solid that stays as part of the plaster. Now over time there may still be some slower curing or water with bicarbonate migration that converts more hydroxide into carbonate so basically a slower version of what you experienced during startup. In that situation, the pH will rise and acid addition will lower both pH and TA.
However, the pool may also have carbon dioxide outgassing though that should be lessened at a lower TA level. With carbon dioxide outgassing, you would see a similar effect that you add acid and the pH and TA get lowered. Basically, the process of carbon dioxide outgassing has the same apparent result to the water as the plaster curing in a bicarbonate start-up. This is because the net result of the two equations I showed earlier is the following:
2Ca3•SiO5 + 3HCO3- + 4H2O --> 3CaO•2SiO2•4H2O + 3CaCO3(s) + 3OH- + heat
Tricalcium Silicate + Bicarbonate Ion + Water ---> Calcium Silicate Hydrate + Calcium Carbonate + Hydroxide Ion + heat
Soft Uncured Plaster + "TA" + Water ---> Hard Cured Plaster + Hard Limestone + "High pH" + heat
When carbon dioxide leaves the water it effectively remove carbonic acid from the water so looking at this from the point of view of bicarbonate ion it is like the following:
HCO3- ---> CO2(g) + OH-
Bicarbonate Ion ---> Carbon Dioxide + Hydroxyl Ion
So the two processes are indistinguishable in terms of the water chemistry and the need for adding acid to lower the pH that also results in a lowering of TA. Another way to look at it is that with the bicarbonate startup carbon dioxide is getting incorporated into the plaster as carbonate which is why the net effect on water chemistry is the same as carbon dioxide outgassing:
2Ca3•SiO5 + 3CO2 + 4H2O --> 3CaO•2SiO2•4H2O + 3CaCO3(s) + heat
Tricalcium Silicate + Carbon Dioxide + Water ---> Calcium Silicate Hydrate + Calcium Carbonate + heat
Now if one does not maintain good water chemistry so that the water is not saturated with calcium carbonate, then two things could happen. One is that any additional curing that produces calcium hydroxide could have that go directly into the water raising the Calcium Hardness (CH) and raising the pH and TA such that acid lowers both (so the net result is a rise in CH) which I designate below as "traditional plaster curing" though it's most extreme with an acid startup. Another thing that could happen is that calcium carbonate could dissolve into the water which raises CH, pH and TA with the main distinction from the calcium hydroxide situation that the pH doesn't rise as much so after acid addition there is a net rise in TA. I summarize these net effects below:
PROCESS .............................. CH .... pH .... TA .... TA (after acid to maintain pH)
Bicarbonate Plaster Curing ......... 0 ...... + ...... 0 ....... - ... one carbon dioxide replaces two hydroxide as carbonate plus water
Carbon Dioxide Outgassing ........ 0 ...... + ...... 0 ....... - ... carbon dioxide leaves the pool
Traditional Plaster Curing .......... + ..... ++ ..... + ...... 0 ... calcium hydroxide dissolves into water
Calcium Carbonate Dissolving .... + ...... + ...... + ...... + ... calcium carbonate dissolves into water
In the ideal bicarbonate plaster curing situation, every 4.7 ppm TA drop after balancing pH with acid corresponds to 10 ppm CH equivalent of calcium carbonate formed in the plaster (but of course you don't see a CH change because the calcium remains in the plaster as solid). You'll know you have the best possible plaster startup when the CH doesn't rise at all and you do not see plaster dust.