Initially reports were that he self-quarantined, only later was it reported that he went bowling etc.
According to this story it was police investigation that revealed his travels.
The initial reports I saw were that he "self-monitored," not quarantined. Reports that he went bowling in Williamsburg were published even before his Ebola test results were back. From the NY Post itself (link):
Craig Spencer, who was was suffering from Ebola-like symptoms — a 103-degree fever and nausea — spent Wednesday night bowling in Williamsburg, the sources said. He used Uber taxis to get there and back.
. . .
Test results should be available in the next 12 hours, they added.
As health officials wait for the results to come in, the case is being treated as if it were already confirmed, according to council member Mark Levine, who represents Spencer’s neighborhood.