Any action you spend on her typically counts as spending time with her and will improve your relationship. With Evelyn, all your chances to spend time with her are in the afternoons.
You don't have to break off her "arrangement," but every time they meet (they only meet if you watch them), she slips one step further away from you. If you get into a relationship with her, she'll break up with Thaddeus behind the scenes, even if you've done nothing to stop them.
You can most easily test your relationship with Evelyn by giving her a massage. The lower she lets you go, the closer you are to hitting the jackpot.