How would you feel if you left your phone in your significant others car and or place by accident and an hour later you come back only to find it being disabled for 5 mins (this happens when someone tries to get into your phone but enters the passcode wrong too many times)? Even if they say they trust you but they just have a huge curiosity and would do it whether was their girlfriend or not. I had nothing to hide but I feel like my privacy has been violated, because I'm an open book so doing it behind my back just made me upset.
I'd be annoyed too. All she has to do is ask and I'd rather hand my phone to her right in the spot. Lurking around and acting secretive though means there is no trust, and it will also make it harder for you to trust him.
Best you can do is talk to him and tell him what you think. Better to do that before these behaviours continue to surface and worsen the relationship.
The only stuff worth hiding on my phone is some of my anonymous questions from more than half a year ago. Honestly, I'm not sure there's any point in breaking into it... so I don't see why they'd want to do that.