So the Alexa app will connect to his library through his phone even though I’m paying for it?
The short answer is yes.
I don't even think it will need to use his iPhone, he will just log in to Apple Music with his Apple ID.
With Family Sharing his listening history will be tied to his Apple ID, and your history is tied to yours.
So not only are the libraries separate, but the likes, dislikes, skips, "hey Siri never play this song again," are all separate.
It's exactly the same as if he paid for his account and you paid for your account.
If it's like Spotify, his Alexa device will need to be set up with his own Amazon account, and then the Apple Music skill will be installed and signed to his Apple ID on his Amazon account through the Alexa app. This will let him use his own Apple Music account.
The echo will use the Apple Music library with the Apple ID that's signed into to the Amazon account the Echo is active on.