Not plural, Will - it's a possessive apostrophe.
The implication/inference is that this residence belongs too The Mattsons.
Although the family likely consists of multiple individuals, the collective ("family") name for that particular group is singular (In the same vein that we consider a "Herd" of cattle, rather than a "HerdS" of cattle - many cattle, just one herd!). I would therefore suggest that 's is indeed correct (grammatically speaking!)
...But I'm prepared to be corrected/mocked/scorned/flamed/publically humiliated as necessary!
(Nice work, Bill!)