Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Confusion
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Airspace Structure; Chart Or Publication; Procedure
Departing out of JAC; clearance was GEYSR5 departure climb to 16;000 ft. then as filed; we were to go out to NALSI crossing at 14;000 ft.; the turn was a very tight 180 degrees and the autopilot started turn before reaching the fix; at 11;800 ft. was able to keep mountains in sight; and directed flying pilot to widen out turn radius and increase climb rate; same time tower acknowledges terrain clearance warning. We got no GPWS warnings and had plenty of airspace to compensate which I acknowledged to tower; there was no issue with ATC.My suggestion is to have NALSI a flyover fix; especially in IFR; or program the FMS to make it a fly over fix and add that to our briefing. There was weather moving in to the area but we were able to maintain visual with the mountain peaks to avoid. Rest of flight was uneventful.
Pilot reported that ATC issued a terrain clearance warning while aircraft was turning in the vicinity of mountains.