Ann had been observing Alex for a while, or it's better to say that from the moment Luna entered.
Ann knew that Alex had this strange interest in Luna.
She knew about that from the moment Alex had seen Luna.
It was quite apparent to her that Alex was interested in Luna.
Now, he was not romantically interested in Luna, she knew that, but he was interested nonetheless.
So, when Luna offered the Association in exchange for letting her live with them, Ann started thinking of things differently.
'We have Maximus to help us out in the political stuff, but wouldn't it be good to have power of our own?'
Ann knew that Max could help them with almost everything related to politics and all, but having an Association under you was different.
To top it off, they will get a competent subordinate like Luna.
Although Ann didn't want to accept it, she knew that Luna was better at political strategies than her.