No, "Williamses'" refers to something that belongs to all members of the family Williams. If it's just one guy, then you'd say "John Williams' house". This doesn't even really have anything to do with possessives since the plural of Williams is Williamses. Simple as that.
Just confirming this is correct (assuming I haven't misunderstood your use of the word 'belongs'). Williamses is the correct plural, Williamses' is the correct plural possessive.
afaik
Just pray someone doesn't have the last name Williamses, because then I'd be baffled too. Williamseses'!?!