If she is saying she feels like she is being baby sat, or complaining in any way, that would make my red flag go right up. He has not cared one iota, and gets why I have to sometimes. It's just the new normal of our M. If she is getting ancy about it, you may need to pay even closer attention to things.
I dream of the day when I don't feel like I need to check. I NEED that day, but it isn't here yet. 9 months and that day isn't anywhere near. My WW has been very good about it, except when I point blank ask her if she's heard from, talked to, seen, or anything with anybody she shouldn't. Then she says it hurts her when I ask. She should have thought about the hurt when she had sex with someone that wasn't me, her husband, and sexted to multiple others. The day I don't snoop or check up on her is the day I,I,I,I feel it's no longer needed.
We are so comfortable with it, that I have a funny story... my FWH opened another email account for a hockey pool. He asked my permission and gave me the passwords. we did it together. The other day he was trying to log in, he called out to me...what's my password for the email again? I yelled it back. Obviously I knew because I had been logging in. Meh, it's a small price to pay to get your family back....My FWH doesn't mind at all. He even has me go into his email to find stuff all the time.
All affairs are variations on a theme. No one has 'Beethoven's 5th' to everyone else's 'Chopsticks'.
Stop when YOU feel it is the right thing to do. Just don't let it consume you, like it did me.
Knowing the details doesn't always make you feel satisfied. In my case, it just made me want to burn a perfectly good couch!