I feel like I'm going to be one of the first ones to completely understand where you're coming from. Why did he feel the need to do it behind your back? If he had any worries, could he not have just asked you? Him doing it without your permission shows that he thinks he knows you have something to hide, and would lie to him about it. It sounds like there isn't a lot of trust coming from his end. I understand how you're feeling. It's like a personal insult that he can't trust you like that. You're not upset because he snooped, but how he did it. Totally rational, IMO.
How would I go about it? Ask him if he looked at your phone. Something like, "Hey, did you go through my phone a couple nights ago while I was sleeping or am I just crazy?" If he says yes or no, reply with something like, "I'm sorry if it seems like I'm being suspicious or guarded. Just know that if you ever worry about my faithfulness to you, I will do anything to let you know I am 100% with you. I have no problem with you checking my phone, I have nothing to hide. I just ask that you check with my permission. There's no need to sneak behind me and do it." Somewhere in that general area. I have never experienced this, but that's about how I'd go about it.
And yes, talking to him face to face is definitely a lot better. Go into the situation wondering if he did, not accusing him of doing so. It will keep both your tempers from flaring.
There on the tips of fair fresh flowers feedeth he; How joyous his neigh,
there in the midst of sacred pollen hidden, all hidden he; how joyous his neigh