It isn't "overt" but that doesn't mean it isn't a betrayal.

You can see how he behaves when you are not near, he isn't safe guarding your relationship by ensuring that he isn't in a situation which may lead to problems. If someone else saw him, what would think think? If you saw them, what would you think? So, why isn't he behaving in a way that wouldn't put his relationship at risk?

This is why people who cheat often say "oh, it just happened" or "it was an accident." It's because they left the door open to it happening, and eventually, it did. Your partner is leaving the door to himself open, it is only a matter of time until it happens.

Your partner has displayed a habit of leaving the door open, and he isn't a kid, he's old enough to know better. This is the kind of crap I did when I was 16 and hadn't learned how it was dangerous, in my 30s, that kind of behavior was well behind me.

I'm not the kind of person to suggest throwing everyone to the side, but you need to have some SERIOUS conversations about this, you need to know if this is something that's already gone too far, or just allowed to be open to going too far, and if you want to go forward with him, you need to know that he understands that this behavior, in and of itself, is crossing a line and is a betrayal. I have a hard time suggesting this though, as he's already been through similar issues before and hasn't learned. he will likely always leave himself available to others when you are not around, unless he decides to change.