Citation V/Ultra/Encore (C560)
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 126; Flight Crew Total 3893; Flight Crew Type 2618
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Human Factors; Procedure
We had just departed TEB runway 24 and were climbing via the assigned departure procedure; the Teterboro 1 (TEB1). The TEB1 says 'Climb heading 240 to 1500 (do not climb above 1500); then turn right heading 280; cross TEB 4.5 DME at 1500; then climb and maintain 2000'.When we checked in with New York TRACON we were heading 240 and climbing through approximately 1000 feet. The controller instructed us to turn right to heading 260 (or possibly 270) and climb to 4;000 feet. Having received an amended clearance we disregarded the TEB1 departure and immediately complied with the controller's instructions. The controller 'corrected' us; saying that we should have completed the turn before continuing to climb. She further chastised us for not following the departure procedure.I have no idea what the controller expected us to do. From her comment about following the SID it seems that she wanted us to continue via the TEB1; but that would have contradicted the heading and altitude she had just assigned us. We were not given the Brasher warning or requested to call the TRACON.
CE-560 Captain reported a contradicting clearance from New York TRACON while flying the TEB1 SID.