My fiancé passed away last year. Our deed lists us as "joint tenants with rights of survivorship." To settle his estate, his family wants to pay off his half of the mortgage owed on the property. Does this mean that his beneficiaries would then automatically own his half of the property?
Our condolences. Whether they know it or not, your fiancé's family would be making a generous gesture.
As surviving joint tenant, you own all of the property to which the deed pertains. Your fiancé's family is under no obligation to pay off his half of the mortgage; that is now your responsibility. If they do pay, they are effectively making a gift to you.
Their act of paying off the mortgage would have no effect on who owns the house. You own it, not anyone who might come under the label of your fiancé's beneficiaries.
For more information on joint tenancy, see Avoiding Probate with Joint Ownership.