you don't expect anything from her and you don't need to say anything to her.
If she complains that everyone knowing about the affair is affecting her job, you tell her that it affected you when you were working as well when you were the only person who knew about it.
If she complains some more, just tell her this: "look, I didn't tell any of these people about the affair, what I told OMW was only between her and me, not the rest of the world, what she chose to do with the information was HER choice, if you have a problem about it, speak to her, I'm not going to waste anymore time talking to you about this, this is ridiculous, you're getting mad at me because people at your work know about your affair?! That's really pretty funny, next time don't have an affair and you'll have nothing to worry about!"
And that's it.
Don't be afraid to stand up for yourself, in fact you need to start doing more of it.
And it doesn't matter which affair, the physical or emotional one, if they're both with the same person, really it's just one affair.
Again, as for your question about what you expect her to do, don't expect nothing, why would you?