When Sia "kindly invited" him to join and become one of her members, Achilles was quite creeped out and at the same time strangely excited.
It was then that Achilles discovered something new about himself — he was a little obsessed with mentally unstable women.
He wasn't sure whether this was a good sign or not, but decided to leave it aside for the time being.
Anyway, after careful consideration, he came to an agreement with her that he would not be working under her, rather, he would become something similar to a hired mercenary for her cohort.
This meant that she could not give any direct command to him and all the plans that the cohort would have in the future must be discussed with him firsthand.
The little elf agreed to his condition without hesitation — as long as he was willing to live in her mansion.
Achilles saw no harm in this matter so it didn't take him much time before agreeing.