Date: 201202
Local time of day: 1801-2400
Location: YUM.Airport, AZ
Flight conditions: VMC
Light: Night
Aircraft: Small Transport; Low Wing; 2 Turboprop Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
ATC / advisory: Tower YUM
Second aircraft: Stratolifter (C-135 / 717)
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Situational Awareness; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Runway
Detector: Person Flight Crew
When detected: Taxi
Result: Flight Crew Took Evasive Action
Contributing factors: Airport; Environment - Non Weather Related; Human Factors; Procedure
Primary problem: Ambiguous

Narrative: We were executing a visual approach. Tower gave us notice that there would be a KC-135 aircraft also setting up for an approach on a crossing runway. The approach was uneventful. After landing we slowed to exit the runway at the first available taxiway on the left which was K. As we were making our turn; Tower instructed us to 'exit at the end and taxi to the gate.' Since the aircraft was already in the turn to go on the taxiway; the taxiways are narrow at this airport; and judging that it was safer to continue the turn instead of swerving back on to the runway; we continued to exit. The First Officer immediately responded to Tower's instruction; 'We are turning now.' As we turned on to K; I noticed an aircraft on final for one of the crossing runways. There are two parallel crossing runways at this airport; one runway physically crosses the runway we used for approach and the other only has the approach corridor crossing the runway. As we made our turn from K to A; which is the taxiway paralleling our runway; ATC instructed us to 'hold short the approach end of Runway 21L.' The K Taxiway was inside of the approach hold short markings. We immediately responded that 'we already past K.' Just as we finished our radio call; the KC-135 flew over us and landed on Runway 21L. I believe that there was confusion with ATC not knowing our exact location on the airport surface and as a result safe aircraft separation was compromised. As we approached the airport airspace I believed I saw the KC-135 make its approach and landing. I did not; however; see the aircraft on final for the crossing runway when we were on short final. I believe ATC had a plan for our runway exit; but did not communicate their intentions until it was too late. In hindsight I think that we could have been more specific in our response; 'we are turning now;' and instead we should have responded with a phrase including the word 'unable' in order to better alert ATC of the situation. ATC and pilot situational awareness is always imperative when conducting safe operations.


Second narrative: [Narrative #2 had no additional information.]


Synopsis: An aircraft landed on YUM Runway 26 and exited earlier than ATC expected; at Taxiway K. While crossing Runway 21L a KC-135 flew directly overhead.