I think the fact that she came clean on her own was HUGE. I had to literally track my H, drive 5 hours and catch him in a hotel before he would admit his Affair.
And for her to admit everything, not just this guy but the others, that was a good thing too. Not that she slept with them, but that she could/did admit it to you of her own free will. Some would admit to the one and hide the others...
Wow, you wanted her to come home but I am sure you didn't want the rest of the story to be real.
I would say be cautious about the 'reconcile RIGHTNOW' thing. I mean if you want her to move home I see the value in doing it now. You don't want her finishing her lease living on her own where it would be harder for her to maintain the no-contact clause.
I hear the "Trust but verify" thing a lot here. Puppy is great with all of that stuff after an affair.
I would want some proof that she ended it, can she show you a text/email whatever that shows it? Transparency includes access to her email, cell phone bills, etc etc.
Of course, there would have to be counseling. My H has cheated on me w/3 different people over the last 10 years, each a few years apart. So whatever in her mind or your relationship has triggered her desire to stray, won't go away on its own. It needs to be rooted out and dealt with, IMO.
OK I am writing too much! Just glad for you that she is coming clean and wants to come home. Be cautious, of course, but remember this is what you said you wanted--the truth/details, and for her to come home.
It will not be easy, but just remind yourself what your goal is.