I have tried to find some independent confirmation of the 12,000 number and cannot.
From the NY Daily News "NYS coronavirus total hits 44, with majority still linked to hospitalized Westchester County lawyer at the hub of the ongoing health scare" (updated 03/06 09:02)
at https://www.nydailynews.com/new-york/nyc-crime/ny-westchester-rabbi-with-diagnosed-with-coronavirus-20200306-lokwhdkgwffglfitxo3cca75wy-story.html
"Fink was among the close to 50 New Yorkers under mandatory quarantine across the state, with another 4,000 people currently under precautionary quarantine, according to Cuomo."
and:
"De Blasio said there were currently more than 2,700 New York City residents under home quarantine as part of the city’s “abundance of caution” in fighting the virus."
That is my only source—no clue where they got the number from...