The crux is that plural refers to the people; possessive to the place. And
the sign is on (and thus indicates) the *property*, not the people---some or all of whom may not even be there at any given time (the property though--with the sign--is still there regardless). In other words, if the sign is indeed meant to be plural and refer to the people, then it needs to be on the Millers themselves---not on their *property*.
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