Starting a relationship with this guy, sounds shaky. What you have to know before you go further, is whether he's seriously practicing his recovery. There's a saying in the program "Walking the walk and not just talking the talk".
As a recovering alcoholic we all make slides in getting better, usually because we short ourselves on meetings or working our steps regularly.
Part of our recovery is to admit when we were wrong, which he did, but also to not make excuses for our behaviour. When we admit we're wrong we have to be fully accepting of whatever the consequenses are. His call to an ex while dating you isn't something you should ignore and using the 'excuse' that it's because he felt insecure or rejected isn't something I'd necessarily forgive even if the person wasn't in recovery.
I'm married to a lady that I met in the program. When we met she only had a few years but I could tell they were good years of practicing sobriety.
If you find that you are continually attracted to addictive personalities then you need to seek help for yourself. If for no other reason than to understand us and how we tick. Go to Alanon to help yourself