Faithful of Song of the Lioness and Pounce of Provost's Dog are the same entity but the roles they play are quite different. For the most part Faithful restricts himself to advising, providing comfort, and keeping watch; in combat he may attack Alanna's enemies but it's as a cat, with normal claws and teeth, more to distract than anything else. Most characters are barely even aware that he's something strange. Pounce is openly sentient and supernatural and frequently helps Beka in big, obvious ways. Why the change? He was Pounce a few hundred years before he was Faithful and probably learned from the experience. Beka wasn't a mage and couldn't defend herself against many magics, unlike Alanna. Alanna, finding that he was absent, could always carry on with a shrug, while Beka was dependent to a point on him and worried whenever he was gone. He meddled enough when with Beka that the gods had him leave the mortal plane - so, he learned a lighter touch.
Why didn't Duke Roger's image magic work as well on Alanna as it did on everyone else (even before her Ordeal)? Because it was made in the image of Alan the boy, not the girl that Alanna actually was. Also helps to make Alanna's inexplicable, Gut Feeling suspicion of him early on more plausible.
Extra dose of Fridge Brilliance, since this probably also explains why he flipped out when her true gender was revealed in their duel. He realized that was why she had always suspected him/been semi-immune to his magic and it pissed him off.
Remember that poor dust spinner outside the prison in Bloodhound and how relieved it is that it can finally shed years and years' worth of human misery into Beka's ears? Well unless the prison moves, once Beka leaves Port Caynn it's going to start collecting pain all over again, and goodness knows how long it will be before it has a way to get rid of it.