Should I tell my ex about a relationship I had while we were apart?

My ex and I broke up on good terms. We were, and still are, in love and sometimes still act as a couple. We aren't together due to personal factors in both our lives right now but have already told each other that if life allows it we'll be back together.
I've never had a relationship aside from my ex, never even kissed a guy. So when we broke up I felt a sense of freedom. Despite being in love with him, I began a friends with benefits relationship with a guy. My ex knew the guy was my friend but I told him there was nothing between us, which is a lie, we'd sext every other night and had phone sex twice.
I feel like a hypocrite because I already got mad at my ex for taking a female friend of his to the movies and told him he needs to think more about how he treats the opposite sex and how it might be seen to others, yet I'm over here flirting and having phone sex with another guy.
I've broken off the friend with benefits relationship and don't even speak to the guy anymore, but I have told my ex about a few things the guy did that I found uncomfortable, things that I didn't give the "Okay" for in our relationship. He asked if I did anything to lead up to these things and I said no, another lie.
I don't plan on starting any more FWBs or relationships until I'm either totally over my ex or back with him so it won't matter. I don't know why I did these things besides that I felt lonely and I know I screwed up.
I know if my ex found out I had a friend with benefits behind his back it would hurt him to the point where he'd probably totally give up on ever being with me again, but at the same time, he broke it off with me and told me not to wait for him to be ready.
I don't know what to do, should I tell my ex about the relationship? Or wait until we're actually back together to tell him? Or does it matter at all since we weren't together when it happened?

Should I tell my ex about a relationship I had while we were apart?
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