Rudo seeing his feelings for Amo as something that could change his life and him as a person, shocked by the impact she has on him, shocked that he did it for himself - he invited Amo to join him in life, growth, path to become better people.
When looking for her, Rudo never stopped to doubt why Amo was "worth it". She was a stranger, even an enemy. An enemy he shown no mercy to, which he quickly regretted but still - who was she to him? Noone.
And Rudo didnt think he would pick anyone off the street like that. He wasnt in a position to do it - he wasnt like Enjin who, by himself was a support system and had Cleaners to back him up. Rudo couldn't not know this, he himself was just picked off the street by these people - rationally he knew that he couldn't just point at any sad lonely soul and ask Enjin "can we keep them?"
None of this concerned Rudo in that moment. When he reached out to Amo, Rudo didn't think about anything, it was a decision between them, it was a moment between him and this girl. The mechanics, the rational part of it only came afterwards, she was invited to come with them but refused. Rudo must have felt relief when Enjin approved of the offer "oh good he doesn't mind..its not like i could decide something like this for myself"
Feelings of selfish, exclusive attachment is something Rudo is yet to explore. But subconsciously he must know Amo is his person, not like a thing but somebody under his protection first and foremost.
Amo is not mincing her words on her end. "Rudo, Amo wants to be able to help, so she will do her best, okay?", "I'm here to make up for damage Amo caused and to help Rudo", "I want to be where Rudo is", "im going back....to Rudo"
trying to call him when she was being assaulted, crying for him when she was imprisoned. Rudo is the first person to reach out to her, and even though new opportunities presented themselves - its clear Amo intends for Rudo to stay her main person.
she is not scared or shy, she's open to new acquaintances - and Amo IS good at communicating with people
but the wish: "Amo wants to be with someone, wants to feel needed" have been fulfilled by Rudo. His family is nice but it doesn't look like Amo wants to go out of her way to know them. Rudo, who she too, doesn't know enough about yet, is her priority