Some points to consider:
The Agreement between the NATIONAL AIR TRAFFIC CONTROLLERS ASSOCIATION AFL/CIO and the Federal Aviation Administration, or contract, was up for renegotiation in 2003, however, it was extended at that time. The extension time is ending and both sides are preparing for negotiations at this time.
While whatever schedule the controllers were working may have been designed by those controllers, it was, or should have been evaluated prior to being approved by management. If it meets the needs and requirements of the FAA, it should be approved. If it does not meet the needs of the agency, it should be disapproved by management and sent back until it meets the staffing requirements of the FAA.
Every so often assignments to the schedule are posted so controllers will know exactly what they will be working in the immediate future. Each of these postings are also approved by facility management.
The 3 hours and 39 minutes mentioned was probably taken from the position logs. Whenever controllers are working a position they sign on a log. Some of the things controllers do, besides take a break, that does not show up on those logs: Pre brief controllers in training to let them know what might be encountered in the imminent training session, items they should be working on, etc. Debriefing the same controller after the training session. Discussing what happened, how it could have been handled better, or differently. Studying manuals; updating manuals; taking Computer Based Instruction; reading required briefing items from FAA management; team meetings. Briefing the controller that is about to take over the position. (only one controller can be signed on at a time) It can take a few minutes to give a briefing because the airplanes don't stop calling, or flying just because someone else wants to work the position. But again, especially in a facility like N90 there is probably ALWAYS a manager/supervisor there. One of their primary duties is to ensure that the personnel on duty are used efficiently. The supervisor decides who works what positions, how long they will work, who goes on break, and for how long.
Same thing with overtime. The calling in of overtime is a management right/responsibility. Controllers don't just show up and say "pay me" they show up after one or more management officials has determined they are needed. A supervisor must determine if staffing is adequate for what is needed to safely operate the shift and act accordingly.
The number of OTC medications that controllers, like pilots, cannot use while working is extensive. Pretty much anything that cautions against operating machinery is prohibited, and probably more. So, what is merely an inconvience for many occupations, is reason to call in sick for controllers.