Your story right now sounds so similar to J and I's with the girl he's been seeing. He told her that we were separating, they told each other "no relationship, just fun", etc., etc., etc.
Now, couple of months down the road, they are fully boyfriend/girlfriend, and she has this idea that he is monogamous with her because we're supposed to be getting divorced (we're not, we're fully together and loving life, it's just his lie to her). He thought he could just drop her at any point and be okay, but now he's realizing that he really likes her and is missing her a lot since she left for college Thursday. I talked to him about telling her the truth and he said that he did put out feelers, and found that she has no interest in anything but monogamy for both of them. J isn't a monogamous person!! So, it's all tearing him up right now.
Your hubby has got to set it straight now before it goes any further and the emotions get too deeply involved. Waiting will only produce a lot of hurt and drama. Your hubby also likes to push boundaries just like J. Some boundaries are good to push, but some are not. It's hard for people like them to figure out which is okay and which isn't unfortunately. J is slowly learning.
On a side note, J told me the other day that she has wanted to friend request me on FB so she could stalk my profile ("learn about the soon to be ex-wife" in her mind). Boy would she be in for a surprise!!! It's all about how much I love my family (boys and hubby), things we all do together, pics of flowers from hubby the other day, etc. I can guarantee that I would not be censoring my wall for her like he does. All that said to say, make sure you prepare yourself on what to do, say, and how to react should you run into her in town. Be upfront with him about how you would expect to handle things if this were to happen. It may put a little pressure on him to do the right thing and man up with the truth.
Married 12 1/2 years. Female. Straight. New to poly.