I'm pretty sure all formulae implementing abilities increase as though you gained another level in the class, but you don't gain other class features. That's how most casting-progression classes work. Formulae-granting ones give their own progression for formulae known/prepared, so they aren't the proper source to look at I imagine.
It's kind of like how a Prestige class that advances casting would advance the damage of a warlock's eldritch blast, and grants new invocations and the level of invocation learnable, but doesn't necessarily increase their energy resistance or damage reduction (unless the specific PrC grants those things, of course).
