The article itself clarifies that the source of the tip was an employer:
Update: Police in Suffolk County, NY, released the following statement
on Thursday evening:
"Suffolk County Criminal Intelligence Detectives received a tip from a
Bay Shore based computer company regarding suspicious computer
searches conducted by a recently released employee. The former
employee's computer searches took place on this employee's workplace
computer."
Employers have a legal right to review employees' computers and Internet traffic, and if the employee was being released for any reason, it is highly likely that the employer would exercise that right - it's kind of standard to monitor people who are being released, usually to ensure they aren't exfiltrating company data.
(The article is dated August 2013; while the author doesn't time the exact incident, it's reasonable to believe the web searches would have been inspired by the April 2013 Boston Marathon bombing, which used a pressure cooker bomb carried in a backpack. And it's also reasonable to believe that police would have paid attention to such a report in that timeframe.)