This is an interesting question and perhaps a bit awkward to answer. In one sense, their secretive relationship is expected because Chekhov carefully foreshadows it in the exposition of the story. In another sense, it also is expected because the resort of Yalta is infamous for just such secretive relationships ("... immorality in such places as Yalta"). In yet another sense, it is definitely expected because the narrator tells us this is precisely what Gurov does: he starts then ends illicit secretive relationships. The way in which it might be unexpected has to do with the psychological elements of the story as this story is, after all, a psychological examination of the two protagonists' (Anna and Gurov) lives.
Is there a psychological, or even a logistical, reason that we do not expect Gurov to undertake a secretive relationship with Anna? No. He has no allegiance to his wife whom he fears; he has no regard for social or religious moral standards as he has broken each repeatedly before; he has no fear of violating a woman's privacy since he is habitually starting new secretive relationships. Logistically, the relationship is somewhat unexpected because he might be to be thwarted by some difficulty since Anna keeps to herself. We do, however, have reason to think it unexpected for him to continue the secretive relationship since he always gets bored with women and feels them burdensome.
every intimacy, which at first so agreeably ... inevitably grows into a regular problem of extreme intricacy, and in the long run the situation becomes unbearable.
Is there a psychological reason that we do not expect Anna to undertake a secretive relationship with Gurov? Yes. Anna's psychological profile is very different from Gurov's. She is diffident and modest, private, young and inexperienced, and mindful of religious and social moral standards. For all of these reasons, we do not expect her to have a secretive relationship. However, Anna does provide us with an explanation of her "fall" into being "a vulgar, contemptible woman ...." She says her lack of experience made her curious and interested in the results of what she was feeling. Then, over time, she was motivated by feelings of love for Gurov, just as he was motivated by love for her.
I have been tormented by curiosity; I wanted something better. 'There must be a different sort of life,' I said to myself. I wanted to live! To live, to live! . . . I was fired by curiosity ...."