@Josephini,
Playing games is not a good idea. If you make him "prove it to you", you are setting up an unhealthy situation that will make it very difficult to have a good relationship. That would not be fair to him, or good for you.
The fact that he apologized to you means that he cares about the relationship and cares about your feelings. Yes, he messed up. Yes, he understands it. Yes, he wants to fix it and more importantly he wants something real with you.
I don't exactly know what "casually dating" means. Generally when I am dating I talk with my partner about when we are exclusively dating. This is something that you should talk about exclusively. There are people with FWB arrangements who openly sleep with other people. When couples talk about the relationship it solves a lot of problems.
From what you have written... it sounds like there is a possibility for a real meaningful relationship. He obviously cares about you. You have a choice.
If you want a more meaningful relationship. You should accept his apology. Forgive him. It is ok for you to say "this really hurt me", one time... but after that, if the relationship is going to be a good relationship, you should forget it and move on with the relationship as if this never happened.
Of course after that, you should talk about how committed the relationship is. If the relationship is an exclusive, committed relationship... then both of you should say this (with words). No more "FWB" talk... FWB's often sleep around. Committed relationships don't sleep around.
If you can have with a deep meaningful relationship that will make you happy, then it is well worth doing this.
If you don't want this relationship or don't feel you can forgive him, then walk away. There is no shame in leaving a relationship that you no longer want. And it is far better than being in a relationship with someone you are upset with or can't trust.
Either forgive, or walk away. Either work for this new level of commitment you find yourself in, or leave it alone.
Don't play games. Making someone "prove it to you" never ends well.