I'm not sure on the stones specifically, but buffers have a pH they like to buffer at. For NaHCO3 (sodium bicarbonate) that is around pH 8.0. So you can raise the pH of water with NaHCO3 to 8.0, at which point adding more won't increase pH further, only increase KH.
Since the rock will be a carbonate source, it's likely to want to buffer at pH 8.0-8.2. And since your tap water is 7.8, any pH concerns are not worth the time.
Leaving the only real issue as TDS (KH), which simply means you might want to pay some attention to water parameters during water changes. But since your KH is high from the tap, this isn't even going to be an issue worth time unless you wait an extremely long time between water changes.
The rock will continue to affect water parameters while it's in the water. You can increase the rocks affect by lowering the water pH to an acidic state, since this will dissolve the rock faster, meaning it will release it's carbonate source faster. But since you have alkaline water, the rock will likely take years to decades to fully dissolve. That slow rate of dissolution, also means a slow rate of releasing it's contents into the water.
I'm not sure on the specifics of the aquasoil, but since the rock and the tap water have mutual parameters, it's probably the effect of the aquasoil you should be concerned about, not the rock.