boyfriend is a bit immature?

He has his ex on snapchat, and he tells me he keeps her added so that she can see all the videos and pictures of us being happy together on his story, so that it can make her jealous. 
I think it's immature of him to do, and it also makes me a bit nervous since why would he still care about what she thinks after being together for over a year? Should I be worried? And how do I convince him that what he's doing is immature?

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