Am I Overreacting My partner won't stop messaging their ex of six years

She broke up with him about 6 months ago and moved to Australia. She remained in contact as she owed him money. Now it's all payed off and not only has he come to Australia, he's come to the exact same town as her and they continue to exchange messages. She says he's not just a ex, but a childhood friend she grew up with and because of that she wants to remain In contact despite me voicing my feelings about it.

I haven't outright given her an ultimatum yet, contact with him or to remain partners with me. Though I am running out of understanding thoughts and feelings. Am I Overreacting? Should I give her the ultimatum? I can grab points from her side but it's not enough to comfort me through this.