Is this a normal reaction?

Damn, the world sure is full of narcissists these days.

Narcissists generally lack self-awareness and their sense of self-esteem and self-worth depends on how others perceive them. They tend to deny flaws in themselves and blame others for the mistakes they make, since in their twisted parallel universe, they're perfect.

What the guy did - "cheating" on you (as he saw it) and then immediately afterwards accusing you of cheating - is a hilariously blatant example of projection, and narcissists are really keen on projecting. The thing about him graciously offering to forgive you is him adopting the role of victim, which is another classic narcissistic manoeuvre that's about trying to make their victim feel guilt so they'll feel obliged to do what the narcissist wants. Unfortunately for narcissists, they don't feel shame and they know the emotion only an intellectual sense, so they need lots of practice before they can figure out how to reliably induce it in others. Also, the guy is quite young, so he'll still be working on refining his manipulation techniques. Therefore, it's not surprising that he rather comically misjudged his intended victim and didn't slip in the guilt stiletto with as much finesse as he'll doubtless have in a few years.

I guarantee that your life will be better without him in it, and I hope the experience will improve your narcissist early-warning radar.