Remaining person on my both deceased parents bank accounts does it become no longer part of the estate ?

My father passed recently and my parents had me on their bank accounts , mother passed previously . I'm the executor of his will and I have a sister . My father's debts have all been paid . What the bank has told me is that since I am the only remaining person on their accounts that they belong to me and the funds, around $13,000. I have been told since I am the only one remaining on the accounts it is not a part of my father's estate . His will only states distribution of personal property nothing but these accounts . Is what I have been told true or am I supposed to split the funds in these accounts with my sister ? I lawyer who reviewed the will says they are mine. Lost !