Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 64.93; Flight Crew Total 165.43; Flight Crew Type 165.43
Workload; Situational Awareness; Human-Machine Interface; Communication Breakdown; Confusion
ATC Issue All Types; Conflict NMAC; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Procedure; Human Factors
Initial climb from SBA; ATC assigned 8;000 feet. I was hand flying the airplane and leveled at 8;000 feet per ATC instruction. After we leveled I noticed another aircraft on the ND traffic display showing 200 feet below us; right after that I heard ATC asking another aircraft to confirm they are descending. I'm not sure what they replied because we then got the traffic. As the traffic aircraft warning is going off I then noticed the other aircraft had climbed to our altitude of 8;000 feet then we got the TCAS RA descend descend now; I quickly pushed the nose over into the green band. Because of the high work load I over heard the captain saying I got the aircraft in sight and to follow the guidance; I then quickly saw the aircraft out the captain front window also descending into us from the left (around 7;600 [feet]) then we got another TCAS RA to Climb; Climb now; I started pitching up into the green band. I understood our procedures and did exactly that. It was a bit stressful to know our TCAS is trying to help us by getting away from the other aircraft but now that aircraft also doing what TCAS was initially telling us. I believe the heading we were assigned from ATC and the heading the other aircraft was on; ATC incorrectly assigned to someone and it didn't help that the other airplane wasn't following ATC instruction. After the clear of conflict I returned to 8;000 feet then we went over to departure and continue the climb.
Air carrier flight crew reported NMAC during departure climb from SBA airport. Flight Crew took evasive action following TCAS RA guidance.