Most Helpful Guy
I will say one thing here right off the bat; remember your "gut instinct" has nothing to do with your gut at all; it is your BRAIN telling you "this is a problem because _____."
Your trust in him has been broken. Period. Once that trust is gone, there's never any regaining it like you need it. I have recently had an ex break off a three year long relationship with me (fiancé; I had already proposed) because I found out about her having regular contact with a guy I know was trying to sleep with her. Hiding phone calls and text messages. Start a fight with me when confronted about it but never own up to it.
It may very well be that "it's not a big deal" that he's contacting his ex, but you need to listen to that part of YOU that said "he hides them from me, we made it a rule that we wouldn't do that—which means that you've both accepted the damage it will due to one another—and he has STILL continued to do that which is a hurtful thing to you.
Now I never presume to know what your man's true intentions are and/or if he really is hiding anything else other than the texts, but from my own personal experience, when she kept doing something that she knew hurt me and tried to deflect the consequences of her actions back onto me and blame ME for being upset about what she'd agreed to stop doing; agreed that she understood "why" it hurt me—it was because she really was hiding the fact that she'd been sleeping with him and she threw away our entire family rather than admit her wrongdoing.
So it may be that there's something bigger that he's hiding from you and that's why he immediately deflects back onto you that which he knows he shouldn't be doing; or it could be that it really is just messaging her, but YOU need to ask yourself NOW; "can I live with someone continues to break my trust?"
I know in my situation my soul has literally died from the loss of my family and the woman I thought I was supposed to spend the rest of my life with, but I will NEVER give everything I have to someone who throws it in my face that they're breaking my trust again.
Best of luck to you!