C560 Captain reported misrigged engine throttle cables caused an dual inadvertent inflight shut down of the engines. Successful restarts were made and the flight crew returned to departure airport.

Narrative

I was the Pilot Flying on this leg to ZZZ from ZZZ1. Captain was the Pilot Monitoring and on the radios. We were descending through about 11500 ft. when I pulled the power levers to idle to begin slowing for the 10000 ft./250 kts speed limit. As we were slowing down; I lightly pulled on both power levers to ensure that they were at idle. After doing so; the right engine started spooling down and then several right hand engine annunciations came on. I made sure that the right power lever wasn't past the shutdown gate and it was in its normal position. I moved it forward a little bit higher than idle to make sure. I didn't notice anything abnormal with the power lever. Captain and I called the right engine shut down and then the Captain proceeded to attempt a restart; while I kept flying the aircraft. It looked like after the right starter button was pushed; all the avionics screens went dark. The only things I noticed to be illuminated were the N1 gauge and the starter light. I'm not sure what else remained on. The right engine spooled back up. I flew with the standby instruments.Then suddenly the left engine spooled down. I had not touched the power levers since I moved the right lever forward a little. I don't know why the left engine spooled down. The Captain then pushed the left starter button and it came back online. Shortly after; our avionics suddenly came back on. ATC called with a normal instruction to fly a heading; with which we [requested priority handling] asking for immediate landing at ZZZ. At this point; we had both engines running and all avionics seemed normal. ATC asked for souls on board and fuel remaining. We flew a visual approach to landing on Runway XX making sure to stay away from idle until almost touching down and then rolled to the end of the runway. On the ground; we called ZZZ Approach saying that we were safely on the ground and we could cancel IFR. We parked and unloaded the plane; the passengers didn't seem to notice anything abnormal. I didn't hear any comments made other than the normal conversations at the end of a trip. After the passengers left; the ZZZ fire trucks arrived with Airport Ops. I was in the plane cleaning up and securing. The Captain was outside talking to Ops and on the phone. I didn't notice anything abnormal on the post-flight. After finishing in the office; the Captain called ZZZ Approach on the way home. ZZZ Approach commented that we stayed calm and that they were glad we were on the ground safely. After investigation by Maintenance; it was found that the cabling to the engines were not set properly; leading to the ability to move into cutoff without going past the gate on the throttles.