No, people are instructed to self-quarantine merely for being exposed to an infected person. The large majority of those people are not expected to eventually test positive.
https://www.nytimes.com/2020/03/04/us/coronavirus-new-hampsh...
A very similar test allocation might also be running in America without anyone but a few experts taking notice. Here in Germany it has technically been on the news but it was completely drowned out by the pointless shouting match between "it cannot be worse than a cold" (because it would interfere with my precious vacation plans) and "our healthcare wouldbe just as overwhelmed as in Wuhan" (because, I don't know, maybe I'm just not racist enough to assume that it will somehow only be bad in China)