I think Azul really appreciates the kindness Andy shows him, as well as all the sincere compliments she gives him indirectly.

He’d just blush with happiness when Andy shows him kindness and attention.

Knowing Azul, at first, he'd be wary of it, thinking the Prefect is hiding something behind all that kindness. But he would quickly realize that Andy is purely sincere in all her actions, so he’d be less suspicious and would accept her kindness, even if he’s sometimes a little reluctant.

Andy, being very compassionate, would understand Azul after his overblot in Book 3, so she’d show him a lot of sympathy.

(Yes, even though he literally tried to enslave the first-years to work in the Mostro and risked making her homeless…)