Hi Omino_del_Bosco! Great question. In the First Edition, the small Beasts (they're called Nuisances in 2e to help with the clarification) move during the Tempo Change when the monster does, typically either moving in range of a scavenger or attacking.
In 2e, Nuisances still act during the Tempo Change, but with the new card grid system, they don't immediately move to where the scavengers are, and they might prioritize different targets when on the battlefield (regular Gristlebears are likely going to attack Ancorhynch instead of the scavengers, for instance). Also, in 2e, at the end of each scavenger's turn, the monsters/nuisances get a brief opportunity to respond, and if the scavenger is out of reach of the monster, nearby Nuisances might activate instead.
I'm excited to get the game into your hands!