When someone checks through their partner's phone it's for no other reason other than a lack of trust. You said you trust him, but in the same sentence you say you were checking through his phone to "make sure"... well if you trust him, wouldn't you be sure? I don't want to make the impression that I'm blaming you for anything, but I think you need to be more honest with yourself and admit that you don't actually trust him. Otherwise you wouldn't have looked and you wouldn't have found anything. Something made you feel an instinctual need to check through his phone and it's clear you found something you didn't want to see, and now you're stuck.
Everyone classifies cheating in different ways. Some people think watching porn is cheating.... other people have very liberal views on monogamy and think anything except sex is OK... It can mean so many different things for different people and because of that, it's imperative to have these discussions with your partner of what your boundaries and expectations are. If he doesn't think happy ending massages is cheating, then in his mind he isn't cheating. But if you think it is cheating, then it's obviously cheating to you. The difference in expectations between you and your partner is the issue here, not necessarily what's been done.
You need to discuss this with him. He may try to turn the table onto you about looking through his phone, but that's classic minimizing behavior and going through his phone is not as bad as cheating on a partner. So if you believe what he did constitutes as cheating, I think you need to take some time to think about what to say to him, and what you want to do about it. Is this a deal breaker for you or do you think you can move past it? Is this something you would tolerate if he does it again, or do you think he can respect your boundaries and abstain from seeking out happy ending massages?
You need to think about what is best for you and what you want from a relationship, because if this behavior is unacceptable to you, then you may need to find someone else to be with who agrees with you and has the same boundaries and expectations as you do.
"Caring is not an advantage."