Mixed up Contacts

So basically my mom gave my aunt her old iPhone 4. However, any contacts my aunt deletes one the old phone affects the contact list on my mom's currenr iPhone. I think it has to do with the fact that the iCloud account and iTunes account on both phones are still the same one aka it's both my moms . So should I ask my aunt to log out from iCloud and iTunes on the old phone or Can I do something else to help .

Ps my aunt and my family arent in the same country at the moment

AND

my aunt is totally blur about using an IPhone as she always uses androids