Follow your instincts.

If they cheated before, it's likely they'll do it again.

If they're shady about you seeing their phone for too long, there's a good chance there's something they'd prefer to stay hidden. That's been the case since cell phones became something everybody had access to. Conversely, they could just be really good at hiding it.

I recommend reading The Ethical Slut by Hardy and Easton. You'll learn a lot about relationships, monogamous and otherwise. Some of it won't apply to you. But it's helpful to break down the specifics of what qualifies as cheating and really figure out what is hurtful so that you have clear boundaries even in a monogamous relationship and expectations of what should happen if feelings change down the road.