Ce-560 captain reported a contradicting clearance from new york TRACON while flying the TEB1 SID.

Attributes
ACN	1444505
Time
Date	201704
Local Time Of Day	0601-1200
Place
Locale Reference	TEB.Airport
State Reference	NY
Environment
Flight Conditions	Marginal
Light	Daylight
Aircraft 1
Make Model Name	Citation V/Ultra/Encore (C560)
Operating Under FAR Part	Part 135
Flight Phase	Initial Climb
Route In Use	Vectors SID TEB1
Flight Plan	IFR
Person 1
Function	Captain Pilot Flying
Qualification	Flight Crew Air Transport Pilot (ATP) Flight Crew Flight Instructor Flight Crew Instrument Flight Crew Multiengine
Experience	Flight Crew Last 90 Days 126 Flight Crew Total 3893 Flight Crew Type 2618
Events
Anomaly	ATC Issue All Types Deviation - Procedural Clearance Deviation - Track / Heading All Types

Narrative:

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.

Original NASA ASRS Text

Title: CE-560 Captain reported a contradicting clearance from New York TRACON while flying the TEB1 SID.

Narrative: 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.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.