Also "younger" here, no I wouldn't show DH my phones because he saw something. I'd explain what it was, unpick why he felt uncomfortable and then decide if I should show him my phone.
My phone IS an extension of me. It has my bank accounts, my financial information, my notes, my shopping lists, my emails, my orders, my messages, my photos, my medical history ....
So no one has free access to it. Not my kids, not DH, no one but me. And I extend that to other people.
I'd need far more than "oh I saw briefly a notification that made me uncomfortable" why does someone elses piece of mind override mine? It doesn't. Not when I know I'm not doing anything I shouldn't.
I'm more likely to lock DHs phone/computer when it's left unlocked than pick it up and look through it.
You need to leave this relationship