I've played around quite a bit with pets recently, and my experience is that a pet will not deliberately seek out and attack a monster that is attacking the PC unless the PC attacks them back. If they wander adjacent to a hostile monster, they might attack it, but they might not, or they might only a couple turns later.
OTOH, I'm pretty sure that I have had pets save me from paralysis deaths before where I had actually engaged the monster first.
Hoping to win with every class, doomed. Archer, Barbarian, Bard, Beastfighter, Druid, Elementalist, Farmer, Fighter, Monk, and ULE Priest down.