How do cross-class abilities scale?

I am leveling an Arcanist as my first character and looking to add 4-8 levels of Conjuror to supplement my current abilities (Stone has a stronger potency than Ruin, Aero would combine well with Bio to wither opponents away, and Protect looks like a great thing to have in general.)

My question is, if I get to level 8 of Conjuror then switch back and continue leveling Arcanist (currently 16), would my use of Aero and Stone be treated as level 8 skills since their origin class is only level 8, or would they be treated as level 16 skills since Arcanist would be my active class?

Or do abilities even scale with class level at all?

First of all you can't use Stone as a conjurer, you need to read the toolbar on the abilities. All skills have an affinity which states which classes/jobs are able to use the skill. Stone only usable be conjurer and white mage.
Aero on the other hand you will be able to use and since skills work with potency it will be stronger the higher your level and better your gear.

Abilities scale. 150 potency is 150 potency, whether it's cross-class or not.

What you don't get with cross-class abilities are class traits that improve them (e.g., the trait that takes Stoneskin from 10% to 18% for CNJ) and ability points that boost the power of it (e.g., using Cure on a class that has a low Mind).

So Aero will be roughly as effective for an ACN as it will for a CNJ, since there are no CNJ traits that boost it, and you'll have about the same INT (possibly more, depending on how you allocate your points). Protect gets less effective at level 16, when CNJ gets the Proshell trait to increase magic defense as well, but the Defense portion will still be roughly as effective as it is for a CNJ.

So abilities scale directly with potencies and their effectiveness is not determined by levels?

Sweet, thanks.