What either of them really thought is maddeningly difficult to figure out, since she lied so much to him and he denied so much to himself about her.
This I'm confident of: the killer knew before she left Mesa that Mimi was NOT the one. I really don't think she ever felt threatened by Mimi, Cancun or not.
Lisa was the threat, start to finish. The killer put her all into destroying that relationship. By February 08 she thought she had finally succeeded.
But no. Travis begins expressing regrets about Lisa in March and never stops. Soon after the killer leaves Mesa Travis' regret about Lisa greatly intensifies. He even tells Chris at one point that he's chasing Mimi to help him try to forget about Lisa. That he's angry with himself for not being able to forget her, but that he just can't.
Their behavior towards each other was shaped by their attitudes and beliefs. Travis kept believing that the killer had to have some kind of conscience, and kept trying to account for her behavior and motivations from that angle, trying to see a logic that just wasn't there.
Arias could assess Travis and his feelings towards the people around him, and vice versa, and act in what she saw as her best interests, but she probably could not understand Travis' reaction, because he had a conscience and she didn't.