You say you've moved out of the home, but it's not clear if you've actually divorced, and even if you did...what is your ex telling people?
Some people don't divorce. Their lives, their rules, but if the relationship is still codified by marriage, a spouse remains the next of kin, even living someplace else. A couple married men offered to date me after I became widowed. I noped right out of those situations, not because of morality, but owing to practicality: at my age, I wasn't going to develop feelings for a man and care for him in his later years and have everything he owned left to his still-wife. Or your ex cold be telling people you're still married, and you just live closer to your job.
I would have been more blunt than you, probably writing something such as, "Yes, that's why we're now divorced."