I think your H has just had the same talk with you that my W has had with me recently.
It is a real turning point but as you and I both know, it may or may not be the "end" of the affair. She will try to pressure him, just like OM is pressuring my W, and it's likely that some of the pressure will sink in and your H will have moments where he is unsure again. Just be ready for all this and remember that you are in this for the long haul. You need to do exactly what you said you'd do, detach, stay OUT OF HIS cell phone records and keep on with the positive outlook.
Him opening up to you is the more important thing than exactly what he said or does right now. The fact that he is starting to trust YOU is good but doesn't mean you need to jump right back in and trust him. That also doesn't mean you have to think everything he says is a lie either. You just take things as they come and do your best to live according to your own goals and desires.
I think you did well and will keep up with you. You seem to be in a really similar place so your story is of particular interest to me.