Light Transport; Low Wing; 2 Turbojet Eng
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor
Confusion; Situational Awareness; Human-Machine Interface
Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Clearance
Chart Or Publication; Human Factors
We were assigned and on the NAPAA4 Departure off Runway 19R at APC. During pre-flight and once again prior to departure we (as per SOP) confirmed the runway and SID was properly loaded into the Dual FMS. After takeoff; during the climb; I was 'heads down' as I was PNF and was just assigned a frequency change from the Tower to Departure Control while at the same time we encountered a TCAS for VFR traffic off the parallel runway (NOT DUE TO ANY NAVIGATIONAL ERROR IDENTIFIED IN THIS REPORT). During the scan for traffic and putting in the new frequency into the FMS; I noticed we were making a longer left turn than I anticipated. I said to the SIC (in left seat flying the aircraft) why is it turning so far and where are we going? We both looked at the SID displayed as well as the FMS and it was evident the FMS decided to sequence us to our next fix - SAC VOR and in doing so commenced a 'smart turn' in that direction.Upon contacting OAK departure; they verified our position/altitude and shortly thereafter contacted us and said 'Just so we are on the same page; you made a left turn after departing APC towards SAC and did not complete the SID.' I responded that yes; we were looking into the FMS turn as we had verified that the SID was loaded correctly in the FMS.Upon completing our day; we decided it was best to get both OAK and APC Tower on the phone to discuss. Both controllers appreciated us contacting them and mentioned that this was not the first time they have seen this happen with the NAPAA4 departure and they were going to look into it. Both controllers indicated since safety was not an issue; they were not interested in any action on us. In addition to the above discussion with ATC; I am also going to contact Collins and/or Jeppesen in regards to a possible issue with the database and/or SID for the NAPAA4 departure.
Pilot reported an unexpected track heading deviation during departure from APC airport while on the NAAPA4 SID.  Reporter stated the SID was properly loaded in the FMS; yet the aircraft turned the wrong heading.